Journal Articles
1. Evolution of multi-phase modes for nonlinear dispersive waves, M.J. Ablowitz and D.J. Benney, Stud. Appl. Math., 49 (1970) 225-238.
2. Applications of slowly varying nonlinear dispersive wave theories, M.J. Ablowitz, Stud. Appl. Math., 50 (1971) 329-344.
3. Approximate methods for obtaining multi-phase modes in nonlinear dispersive wave problems, M.J. Ablowitz, Stud. Appl. Math., 51 (1972) 17-55.
4. Semi-resonant interactions and frequency dividers, M.J. Ablowitz, B.A. Funk and A.C. Newell, Stud. Appl. Math., 52 (1973) 51-74.
5. Decay of continuous spectrum for solutions of Korteweg–deVries equation, M.J. Ablowitz and A.C. Newell, J. Math. Phys., 14 (1973) 1277-1284.
6. Method for solving Sine-Gordon equation, M.J. Ablowitz, D.J. Kaup, A.C. Newell and H. Segur, Phys. Rev. Lett., 30 (1973) 1262-1264
7. Nonlinear-evolution equations of physical significance, M.J. Ablowitz, D.J. Kaup, A.C. Newell and H. Segur, Phys. Rev. Lett., 31 (1973) 125-127.
8. Coherent pulse propagation, A dispersive, irreversible phenomenon, M.J. Ablowitz, D.J. Kaup, and A.C. Newell, J. Math. Phys., 11 (1974) 1852-1858.
9. Inverse scattering transform - fourier analysis for nonlinear problems, M.J. Ablowitz, D.J. Kaup, A. C. Newell and H. Segur, Stud. Appl. Math., 53 (1974) 249-315. ∗This has been judged a citation classic by Current Contents (see Current Contents, June 7, 1982, Vol. 13, No.23).
10. Nonlinear differential-difference equations, M.J. Ablowitz and J.F. Ladik, J. Math. Phys., 16 (1975) 598-603.
11. Note on resonance and nonlinear dispersive waves, M.J. Ablowitz, Stud. Appl. Math., 54 (1975) 61-70.
12. Inverse scattering transform - semi-infinite interval, M.J. Ablowitz and H. Segur, J. Math. Phys., 16 (1975) 1054-1056.
13. Resonantly coupled nonlinear evolution equations, M.J. Ablowitz and R. Haberman, J. Math. Phys., 16 (1975) 2301-2305.
14. Nonlinear evolution equations—2 and 3 dimensions, M.J. Ablowitz and R. Haberman, Phys. Rev. Lett., 35 (1975) 1185-1188.
15. Asymptotic solutions and conservation laws for the nonlinear Schrodinger equation I, H. Segur and M.J. Ablowitz, J. Math. Phys., 17 (1976) 710-713.
16. Nonlinear differential–difference equations and fourier-analysis, M.J. Ablowitz and J.F. Ladik, J. Math. Phys., 17 (1976) 1011-1018.
17. Nonlinear difference scheme and inverse scattering, M.J. Ablowitz and J.F. Ladik, Stud. Appl. Math., 55 (1976) 213-229.
18. Solution of a class of nonlinear partial difference equations, M.J. Ablowitz and J.F. Ladik, Stud. Appl. Math., 57 (1977) 1-12.
19. Nonlinear evolution equations, continuous and discrete, M.J. Ablowitz, SIAM Review, 19 (1977) 663-684 (invited article).
20. Asymptotic solutions of Korteweg–deVries equation, M.J. Ablowitz and H. Segur, Stud. Appl. Math., 57 (1977) 13–44.
21. Exact linearization of a Painlev´e transcendent, M.J. Ablowitz and H. Segur, Phys. Rev. Lett., 38 (1977) 1103-1106.
22. Solitons and rational solutions of non-linear evolution equations, M.J. Ablowitz and J. Satsuma, J. Math. Phys., 19 (1978) 2180-2186.
23. Lectures on inverse scattering transform, M.J. Ablowitz, Stud. Appl. Math., 58 (1978) 17–94.
24. Non-linear evolution equations and ordinary differential-equations of Painlev´e type, M.J. Ablowitz, A. Ramani and H. Segur, Lett. al Nuovo Cimento, 23 (1978) 333–338.
25. Note on Miura transformation, M.J. Ablowitz, M.D. Kruskal and H. Segur, J. Math. Phys., 20 (1979) 999-1003.
26. Evolution of packets of water-waves, M.J. Ablowitz and H. Segur, J. Fluid Mech., 92 (1979) 691-715.
27. Explicit solutions of Fischer’s equation for a special wave speed, M.J. Ablowitz and A. Zep- petella, Bulletin of Math. Bio., 41 (1979) 835-840.
28. Transverse instability of one-dimensional transparent optical pulses in resonant media, M.J. Ablowitz and Y. Kodama, Phys. Lett. A, 70 (1979) 83-86.
29. 2-dimensional lumps in nonlinear dispersive systems, J. Satsuma and M.J. Ablowitz, J. Math. Phys., 20 (1979) 1496-1503.
30. Resonant nonlinear vibrations in continuous systems. I. Undamped case, M.J. Ablowitz, A. Askar, A.S. Cakmak and H. Engin, Int. J. Nonlin. Mech., 14 (1979) 223-233.
31. Resonant nonlinear vibrations of continuous systems. II. Damped and transient-behavior, H. Engin, M.J. Ablowitz, A. Askar and A.S. Cakmak, Int. J. Nonlin. Mech., 14 (1979) 235-246.
32. Solutions of the Korteweg–deVries equation, M.J. Ablowitz and H. Cornille, Phys. Lett. A, 72 (1979) 277-280.
33. Internal wave-equation describing a stratified fluid with finite depth, J. Satsuma, M.J. Ablowitz and Y. Kodama, Phys. Lett. A, 73 (1979) 283-286.
34. Solitary wave collisions, M.J. Ablowitz, M.D. Kruskal and J.F. Ladik, SIAM J. Appl. Math., 36 (1979) 428-437.
35. A connection between non-linear evolution-equations and ordinary differential-equations of P-type. I., M.J. Ablowitz, A. Ramani and H. Segur, J. Math. Phys., 21 (1980) 715-721.
36. A connection between non-linear evolution-equations and ordinary differential-equations of P-type. II., M.J. Ablowitz, A. Ramani and H. Segur, J. Math. Phys., 21 (1980) 1006-1015.
37. Transverse instability of breathers in resonant media, Y. Kodama and M.J. Ablowitz, J. Math. Phys., 21 (1980) 928-931.
38. Comparison between finite-element methods and spectral methods as applied to bound-state problems, M. Duff, H. Rabitz, A. Askar, A. Cakmak and M.J. Ablowitz, J. Chem. Phys., 72 (1980) 1543-1559.
39. Long internal waves in fluids of great depth, M.J. Ablowitz and H. Segur, Stud. Appl. Math., 62 (1980) 249-262.
40. Remarks on non-linear evolution-equations and ordinary differential-equations of Painlev´e type, M.J. Ablowitz, Physica D, 3 (1981) 129-141.
41. Asymptotic solutions of non-linear evolution-equations and a Painlev´e transcendent, H. Segur and M.J. Ablowitz, Physica D, 3 (1981) 165-184.
*42. The soliton: A significant, coherent nonlinear phenomena, M.J. Ablowitz and A.S. Fokas, Clarkson Innovations, 1 (1981) 2-3 (invited article).
43. Finite perturbations and some special solutions of the Korteweg–deVries equation, H. Airault and M.J. Ablowitz, C.R. Acad. Sc. Paris, 292 (1981) 279-281.
44. Non-linear intermediate long-wave equation - Analysis and method of solution, Y. Kodama, J. Satsuma and M.J. Ablowitz, Phys. Rev. Lett., 46 (1981) 687-690.
45. Linearization of the Korteweg–deVries and Painlev´e II equations, A.S. Fokas and M.J. Ablowitz, Phys. Rev. Lett., 47 (1981) 1096-1100.
46. Perturbations of solitons and solitary waves, Y. Kodama and M.J. Ablowitz, Stud. Appl. Math., 64 (1981) 225-245.
47. The periodic cubic Schr¨odinger-equation, Y.C. Ma and M.J. Ablowitz, Stud. Appl. Math., 65 (1981) 113-158.
48. Note on asymptotic solutions of the Korteweg–deVries equation with solitons, M.J. Ablowitz and Y. Kodama, Stud. Appl. Math., 66 (1982) 159-170.
49. Direct and inverse scattering problems of the non-linear intermediate long-wave equation, Y. Kodama, M.J. Ablowitz and J. Satsuma, J. Math. Phys., 23 (1982) 564-576.
50. On the periodic intermediate long-wave equation, M.J. Ablowitz, A.S. Fokas, J. Satsuma and H. Segur, J. Phys. A - Math. and Gen., 15 (1982) 781-786.
51. Direct linearizations of the Korteweg-deVries equations, A.S. Fokas and M.J. Ablowitz, AIP Conference Proceedings, 88 (1982) 237-241.
52. A direct linearization associated with the Benjamin-Ono-Equation, M.J. Ablowitz and A.S. Fokas, AIP Conference Proceedings, 88 (1982) 229-236.
53. On a unified approach to transformations and elementary solutions of Painlev´e equations, A.S. Fokas and M.J. Ablowitz, J. Math. Phys., 23 (1982) 2033-2042.
54. The inverse scattering transform for the Benjamin-Ono-Equation - A pivot to multidimensional problems, A.S. Fokas and M.J. Ablowitz, Stud. Appl. Math., 68 (1983) 1-10.
55. On the inverse scattering of the time-dependent Schrodinger equation and the associated Kadomsev-Petviashvili equation, A.S. Fokas and M.J. Ablowitz, Stud. Appl. Math., 69 (1983) 211-228.
56. On the inverse scattering transform for the Kadomtsev-Petviashvili equation, M.J. Ablowitz, D. Bar Yaacov and A.S. Fokas, Stud. Appl. Math., 69 (1983) 135-143.
57. Method of solution for a class of multidimensional non-linear evolution-equations, A.S. Fokas and M.J. Ablowitz, Phys. Rev. Lett., 51 (1983) 7-10.
58. On the initial-value problem of the 2nd Painlev´e transcendent, A.S. Fokas and M.J. Ablowitz, Commun. Math. Phys., 91 (1983) 381-403.
59. The direct linearizing transform and the Benjamin-Ono equation, M.J. Ablowitz, A.S. Fokas and R.L. Anderson, Phys. Lett. A, 93 (1983) 375-378.
60. On the inverse scattering and direct linearizing transforms for the Kadomtsev-Petviashvili equation, A.S. Fokas and M.J. Ablowitz, Phys. Lett. A, 94 (1983) 67-70.
61. The inverse scattering transform for multidimensional (2+1) problems, A.S. Fokas and M.J. Ablowitz, Lect. Notes Phys., 189 (1983) 137-183.
62. Comments on the inverse scattering transform and related non-linear, evolution-equations, M.J. Ablowitz and A.S. Fokas, Lect. Notes Phys., 189 (1983) 3-24.
63. On a Backlund transformation and scattering problem for the modified intermediate long-wave equation, J. Satsuma, T.R. Taha and M.J. Ablowitz, J. Math. Phys., 25 (1984) 900-904.
64. Analytical and numerical aspects of certain nonlinear evolution-equations. I. Analytical, T.R. Taha and M.J. Ablowitz, J. Comp. Phys., 55 (1984) 192-202.
65. Analytical and numerical aspects of certain nonlinear evolution-equations. II. Numerical, nonlinear Schr¨odinger-Equation, T.R. Taha and M.J. Ablowitz, J. Comp. Phys., 55 (1984) 203-230.
66. Analytical and numerical aspects of certain nonlinear evolution-equations. III. Numerical, Korteweg–deVries equation, T.R. Taha and M.J. Ablowitz, J. Comp. Phys., 55 (1984) 231- 253.
67. On the inverse scattering transform of multidimensional nonlinear equations related to 1st -order systems in the plane, A.S. Fokas and M.J. Ablowitz, J. Math. Phys., 25 (1984) 2494-2505.
68. On the limit from the intermediate long-wave equation to the Benjamin-Ono equation, P. Santini, M.J. Ablowitz and A.S. Fokas, J. Math. Phys., 25 (1984) 892-899.
69. The direct linearization of a class of nonlinear evolution-equations, P.M. Santini, M.J. Ablowitz, and A.S. Fokas, J. Math Phys., 25 (1984) 2614-2619.
70. A multidimensional inverse-scattering method, A. Nachman and M.J. Ablowitz, Stud. Appl. Math., 71 (1984) 243-250.
71. Multidimensional inverse scattering for 1st -order systems, A. Nachman and M.J. Ablowitz, Stud. Appl. Math., 71 (1984) 251-262.
72. Nonlinear evolution-equations associated with a Riemann-Hilbert scattering problem, A. De- gasperis, P.M. Santini and M.J. Ablowitz, J. Math. Phys., 26 (1985) 2469-2472.
73. Multidimensional nonlinear evolution-equations and inverse scattering, M.J. Ablowitz and A.I. Nachman, Physica D, 18 (1986) 223-241.
74. On the solution of the generalized wave and generalized Sine-Gordon equations, M.J. Ablowitz, R. Beals and K. Tenenblat, Stud. Appl. Math., 74 (1986) 177-203.
75. Note on solutions to a class of nonlinear singular integrodifferential equations, M.J. Ablowitz, A.S. Fokas and M.D. Kruskal, Phys. Lett A, 120 (1987) 215-218.
76. An example of a ∂¯ problem arising in a finite difference context: Direct and inverse problem for the discrete analogue of the equation ψxx + U ψ = σψy , O. Ragnisco, P.M. Santini, S. Chitlaru–Briggs and M.J. Ablowitz, J. Math. Phys., 28 (1987) 777-780.
77. Solutions of multidimensional extensions of the anti-self-dual Yang-Mills equation, M.J. Ablowitz, D.G. Costa and K. Tenenblat, Stud. Appl. Math., 77 (1987) 37-46.
78. On the initial-value problem for a class of nonlinear integral evolution-equations including the Sine-Hilbert equation, P.M. Santini, M.J. Ablowitz and A.S. Fokas, J. Math. Phys., 28 (1987) 2310-2316.
79. Davey-Stewartson-I system - A quantum (2+1) dimensional integrable system, C.L. Schultz, M.J. Ablowitz and D. Bar Yaacov, Phys. Rev. Lett., 59 (1987) 2825-2828.
80. A method of linearization for Painlev´e equations - Painlev´e-IV, Painlev´e-V, A.S. Fokas, U. Mugan and M.J. Ablowitz, Physica D, 30 (1988) 247-283.
81. A rule for fast computation and analysis of soliton automata, T.S. Papatheodorou, M.J. Ablowitz and Y.G. Saridakis, Stud. Appl. Math., 79 (1988) 173-184.
82. Analytical and numerical aspects of certain nonlinear evolution-equations. IV. Numerical, modified Korteweg–deVries equation, T. Taha and M.J. Ablowitz, J. Comp. Phys., 77 (1988) 540-548.
83. Hodograph transformations of linearizable partial-differential equations, P.A. Clarkson, A.S. Fokas and M.J. Ablowitz, SIAM J. Appl. Math., 49 (1989) 1188-1209.
84. Forced nonlinear evolution-equations and the inverse scattering transform, A.S. Fokas and M.J. Ablowitz, Stud. Appl. Math., 80 (1989) 253-272.
85. Interaction of simple particles in soliton cellular automata, A.S. Fokas, E.P. Papadopoulou, Y.G. Saridakis and M.J. Ablowitz, Stud. Appl. Math., 81 (1989) 153-180.
86. Strong coupling limit of certain multidimensional nonlinear-wave equations, M.J. Ablowitz and C.L. Schultz, Stud. Appl. Math., 80 (1989) 229-238.
87. Numerically induced chaos in the nonlinear Schrodinger-Equation, B. Herbst and M.J. Ablowitz, Phys. Rev. Lett., 62 (1989) 2065-2068.
88. Action angle variables and trace formula for D-bar limit case of Davey-Stewartson I, C.L. Schultz and M.J. Ablowitz, Phys. Lett. A., 135 (1989) 433-437.
89. Solitons, inverse problems and nonlinear equations, M.J. Ablowitz, Math. Applic. Comp., 8 (1989) 127-152 (invited article).
90. On homoclinic structure and numerically induced chaos for the nonlinear Schrodinger-Equation, M.J. Ablowitz and B.M. Herbst, SIAM J. Appl. Math., 50 (1990) 339-351.
91. Reductions of self-dual Yang-Mills fields and classical-systems, S. Chakravarty, M.J. Ablowitz and P.A. Clarkson, Phys. Rev. Lett., 65 (1990) 1085-1087.
92. On the boundary-conditions of the Davey-Stewartson equation, M.J. Ablowitz, S.V. Manakov and C.L. Schultz, Phys. Lett. A, 148 (1990) 50-52; condensed version published in Non- linear Evolution Equations and Dynamical Systems pp 29 - 32, Research Reports in Physics, Springer-Verlag, Berlin (1990).
93. On the Kadomtsev-Petviashvili equation and associated constraints, M.J. Ablowitz and J. Villarroel, Stud. Appl. Math., 85 (1991) 195-213.
94. On the hamiltonian-formalism for the Davey-Stewartson system, J. Villarroel and M.J. Ablowitz, Inverse Problems, 7 (1991) 451-460.
95. Numerical homoclinic instabilities and the complex modified Korteweg-de Vries equation, B.M. Herbst, M.J. Ablowitz and E. Ryan, Computer Phys. Commun., 65 (1991) 137-142.
96. Forced and semiline solutions of the Burger’s-Equation, M.J. Ablowitz and S. De Lillo, Phys. Lett. A, 156 (1991) 483-487.
97. Class of stable multistate time-reversible cellular automata with rich particle content, M.J. Ablowitz, J.M. Keiser and L.A. Takhtajan, Phys. Rev. A, 44 (1991) 6909-6912.
98. Dynamics of semi-discretizations of the defocusing nonlinear Schrodinger equation, M.J. Ablowitz, B.M. Herbst and J.A. Weidman, IMA J. Num. Anal. II, (1991) 539-552.
99. On the method of solution to the 2 + 1 Toda equation, J. Villarroel and M.J. Ablowitz, Phys. Lett. A, 163 (1992) 293-298.
100. A new Hamiltonian amplitude equation governing modulated wave instabilities, M. Wadati, H. Segur and M.J. Ablowitz, J. Phys. Soc. of Japan, 61 (1992) 1187-1193.
*101. Numerical homoclinic instabilities in the Sine-Gordon equation, B.M. Herbst and M.J. Ablowitz, Quaestiones Math., 15 (1992) 345-363.
*102. Stable, multi-state, time-reversible cellular automata with rich particle content, M.J. Ablowitz, J.M. Keiser and L.A. Takhtajan, Quaestiones Math., 15 (1992) 325-343.
103. Interaction effects on wavelength multiplexed soliton data packets, A.F. Benner, J.R. Sauer and M.J. Ablowitz, J. Opt. Soc. Amer. B - Opt. Phys., 10, (1993) 2331-2340.
104. A self-dual Yang-Mills hierarchy and its reductions to integrable systems in 1 + 1 and 2 + 1 dimensions, M.J. Ablowitz, S. Chakravarty and L.A. Takhtajan, Commun. Math. Phys., 158 (1993) 289-314.
105. Numerical chaos, symplectic integrators and exponentially small splitting distances, B.M. Herbst and M.J. Ablowitz, J. Comp. Phys., 105 (1993) 122-132.
106. On the inverse scattering transform of the 2+1 Toda equation, J. Villarroel and M.J. Ablowitz, Physica D, 65 (1993) 48-70.
107. Numerical chaos, roundoff errors, and homoclinic manifolds, M.J. Ablowitz, C. Schober and B.M. Herbst, Phys. Rev. Lett., 71 (1993) 2683-2686.
108. On the method of solution of the differential-delay Toda equation, J. Villarroel and M.J. Ablowitz, Phys. Lett. A, 180 (1993) 413-418.
109. Solutions to the 2+1 Toda equation, J. Villarroel and M.J. Ablowitz, J. Phys. A - Math. and Gen., 27 (1994) 931-941.
110. Parametric forcing, bound-states and solutions of a nonlinear Schrodinger type equation, M.J. Ablowitz and S. De Lillo, Nonlinearity, 7 (1994) 1143-1153.
111. Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equa- tion, X.P. Wang, M.J. Ablowitz and H. Segur, Physica D, 78 (1994) 241-265.
112. Homoclinic manifolds and numerical chaos in the nonlinear Schrodinger-Equation, M.J. Ablowitz and C. Schober, Math. and Comp. Sim., 37 (1994) 249-264.
113. Symplectic methods for the nonlinear Schrodinger-Equation, B.M Herbst, F. Varadi and M.J. Ablowitz, Math. and Comp. Sim., 37 (1994) 353-369.
*114. Effective chaos in the nonlinear Schrodinger equation, M.J. Ablowitz and C. Schober, Con- temp. Math., 172 (1994) 253-268.
115. Hamiltonian integrators for the nonlinear Schrodinger equation, M.J. Ablowitz and C.M. Schober, Intern. J. Mod. Phys. C - Phys. and Comp., 5 (1994) 397-401.
116. Multisoliton interactions and wavelength-division multiplexing, S. Chakravarty, M.J. Ablowitz, J.R. Sauer and R.B. Jenkins, Opt. Lett., 20 (1995) 136-138.
117. Integrability, computation and applications, M.J. Ablowitz, S. Chakravarty and B.M. Herbst, Acta Applicande Mathematicae, 39 (1995) 5-37.
118. Data-dependent timing jitter in wavelength-dependent-multiplexing soliton systems, R.B. Jenkins, J.R. Sauer, S. Chakravarty and M.J. Ablowitz, Opt. Lett., 20 (1995) 1964-1966.
119. Numerical-simulation of quasi-periodic solutions of the Sine-Gordon equation, M.J. Ablowitz, B.M. Herbst and C.M. Schober, Physica D, 87 (1995) 37-47.
120. Numerical stochasticity, hamiltonian integrators, and the nonlinear Schrodinger-Equation, M.J. Ablowitz and C. Schober, Three-Dim. Sys.–Annals NY Acad. Sci., 751 (1995) 162- 181.
121. Integrability, monodromy evolving deformations, and self-dual Bianchi IX systems, S. Chakravarty and M.J. Ablowitz, Phys. Rev. Lett., 76 (1996) 857-860.
122. Computational chaos in the nonlinear Schrodinger equation without homoclinic crossings, M.J. Ablowitz, B.M. Herbst and C.M. Schober, Physica A, 228 (1996) 212-235.
123. On the numerical solution of the Sine-Gordon equation. I. Integrable discretizations and homoclinic manifolds, M.J. Ablowitz, B.M. Herbst and C.M. Schober, J. Comp. Phys., 126 (1996) 299-314.
124. The Burgers equation under deterministic and stochastic forcing, M.J. Ablowitz and S. De Lillo, Physica D, 92 (1996) 245-259.
125. On a 2+1 Volterra system, J. Villarroel, S. Chakravarty and M.J. Ablowitz, Nonlinearity, 9 (1996) 1113-1128.
126. Four-wave mixing in wavelength-division-multiplexed soliton systems: damping and amplifi- cation, M.J. Ablowitz, G. Biondini, S. Chakravarty, R.B. Jenkins and J.R. Sauer, Opt. Lett., 21 (1996) 1646-1648.
127. Solutions to the time dependent Schrodinger and the Kadomtsev-Petviashvili equations, M.J. Ablowitz and J. Villarroel, Phys. Rev. Lett., 78 (1997) 570-573.
128. The nonlinear Schr¨odinger equation: asymmetric perturbations, traveling waves and chaotic structures, M.J. Ablowitz, B.M. Herbst and C.M. Schober, Math. and Comp. Sim., 43 (1997) 3-12.
129. Initial time layers and Kadomtsev-Petviashvili-Type equations, M.J. Ablowitz and X-P. Wang, Stud. Appl. Math., 98 (1997) 121-137.
130. On the well-posedness of the Eckhaus equation, M.J. Ablowitz, G. Biondini and S. De Lillo, Phys. Lett. A, 230 (1997) 319-323.
131. On the numerical solution of the Sine-Gordon equation. II. Performance of numerical schemes, M.J. Ablowitz, B.M. Herbst and C.M. Schober, J. of Comp. Phys., 131 (1997) 354-367.
132. Four-wave mixing in wavelength-division-multiplexed soliton systems: ideal fibers, M.J. Ablowitz, G. Biondini, S. Chakravarty, R.B. Jenkins and J.R. Sauer, J. Opt. Soc. Am. B., 14 (1997) 1788-1794.
133. Multi-dimensional pulse propagation in non-resonant χ(2) materials, M.J. Ablowitz, G. Bion- dini and S. Blair, Phys. Lett. A, 236 (1997) 520-524.
134. On timing jitter in wavelength-division multiplexed soliton systems, M.J. Ablowitz, G. Bion- dini, S. Chakravarty and R.L. Horne, Opt. Comm., 150 (1998) 305-318.
135. Multiscale pulse dynamics in communication systems with strong dispersion management, M.J. Ablowitz and G. Biondini, Opt. Lett., 23 (1998) 1668-1670.
*136. The generalized Chazy equation and Schwarzian triangle functions, M.J. Ablowitz, S. Chakravarty and R. Halburd, Asian J. Math., 2 (1998) 619-624.
137. On discretizations of the vector nonlinear Schrodinger equation, M.J. Ablowitz, Y. Ohta and A.D. Trubatch, Phys. Lett. A, 253 (1999) 287-304.
138. The generalized Chazy equation from the self-duality equations, M.J. Ablowitz, S. Chakravarty and R. Halburd, Stud. Appl. Math., 103 (1999) 75-88.
139. On the discrete spectrum of the nonstationary Schrodinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation, J. Villarroel and M.J. Ablowitz, Commun. Math. Phys., 207 (1999) 1-42.
140. A comparison between lumped and distributed filter models in wavelength-division multiplexed soliton systems, M.J. Ablowitz, G. Biondini, S. Chakravarty and R. Horne, Opt. Comm., 172 (1999) 211-227.
141. Solitons and symmetries, M.J. Ablowitz and P.A. Clarkson, J. Eng. Math., Special Edition, M.J. Ablowitz and P.A. Clarkson, editors, 36 (1999) 1-9.
142. Modulated periodic Stokes waves in deep water, M.J. Ablowitz, J. Hammack, D. Henderson and C.M. Schober, Phys. Rev. Lett., 84 (2000) 887-890.
143. On integrability and chaos in discrete systems, M.J. Ablowitz, Y. Ohta, and A.D. Trubatch, Chaos, Solitons and Fractals, 11 (2000) 159-169.
144. A novel class of solutions of the non-stationary Schrodinger and the Kadomtsev-Petviashvili I equations, M.J. Ablowitz, S. Chakravarty, A.D. Trubatch and J. Villarroel, Phys. Lett. A, 267 (2000) 132-146.
145. On a Burgers-Stefan problem, M.J. Ablowitz and S. De Lillo, Nonlinearity, 13 (2000) 471-478.
146. On the extension of the Painlev´e property to difference equations, M.J. Ablowitz, R. Halburd and B. Herbst, Nonlinearity, 13 (2000) 889-905.
147. Optical solitons: perpsectives and applications, M.J. Ablowitz, G. Biondini and L. Ostrovsky, Chaos, 10 (2000) 471-474.
148. Solutions of a Burgers-Stefan problem, M.J. Ablowitz and S. De Lillo, Phys. Lett. A., 271 (2000) 273-276.
149. Resonant nonlinear intrachannel interactions in strongly dispersion-managed transmission systems, M.J. Ablowitz and T. Hirooka, Opt. Lett., 25 (2000) 1750-1752.
150. Quasi-linear optical pulses in strongly dispersion-managed transmission systems, M. J. Ablowitz, T. Hirooka and G. Biondini, Opt. Lett., 26 (2001) 459-461.
151. Long-time dynamics of the modulational instability of deep water waves, M.J. Ablowitz, J. Hammack, D. Henderson and C.M. Schober, Physica D - Nonlin. Phenom., 152 (2001) 416-433.
152. Nonlinear Schr¨odinger equations with mean terms in nonresonant multidimensional quadratic materials, M.J. Ablowitz, G. Biondini and S. Blair, Phys. Rev. E, 63 (2001) 046605-605-620.
153. Incomplete collisions of wavelength-division multiplexed dispersion-managed solitons, M.J. Ablowitz, G. Biondini and E.S. Olson J. Opt. Soc. Am. B - Opt. Phys., 18 (2001) 577-583.
154. Nonlinear feedback shift registers via nonlinear evolution, M.J. Ablowitz, Stud. Appl. Math., 107 (2001) 127-136.
155. Nonlinear effects in quasi-linear dipersion-managed pulse transmission, M.J. Ablowitz and T.Hirooka, IEEE Phot. Tech. Lett., 13 (2001) 1082-1084.
156. Intrachannel pulse interactions in dispersion-managed transmission systems: timing shifts , M.J. Ablowitz and T.Hirooka, Opt. Lett., 26 (2001) 1846-1848.
157. Discrete diffraction managed spatial solitons, M.J. Ablowitz and Z. Musslimani, Phys. Rev. Lett., 87 (2001) 254102-1-4.
158. Discretizations, integrable systems and computation, M.J. Ablowitz, B.M. Herbst and C.M. Schober, J. Phys. A - Math. and Gen., 34 (2001) 10671-10693.
159. Localized multi-dimensional optical pulses in non-resonant quadratic materials, M.J. Ablowitz, G. Biondini and S. Blair, Math. and Comp. Sim., 56 (2001) 511-519.
160. Methods for discrete solitons in nonlinear lattices, M.J. Ablowitz, Z. Musslimani and G. Biondini, Phys. Rev. E, 65 (2002) 026602-1-4.
161. Intrachannel pulse interactions in dispersion-managed transmission systems: energy transfer, M.J. Ablowitz and T. Hirooka, Opt. Lett., 27 (2002) 203-205.
162. Managing nonlinearity in strongly dispersion-managed optical pulse transmission, M.J. Ablowitz and T.Hirooka, J. Opt. Soc. Amer. B - Opt. Phys., 19 (2002) 425-439.
163. Collision-induced timing shifts in dispersion-managed soliton systems, M.J. Ablowitz, A. Biswas, A. Docherty, T.Hirooka, G. Biondini and S. Chakravarty, Opt. Lett., 27 (2002) 318-320.
164. Suppression of intrachannel dispersion-managed pulse interactions by distributed amplifica- tion, T.Hirooka and M.J. Ablowitz, IEEE Phot. Tech. Lett., 14 (2002) 316-318.
165. Analysis of timing and amplitude jitter due to intrachannel dispersion-managed pulse inter- actions, T.Hirooka and M.J. Ablowitz, IEEE Phot. Tech. Lett., 14 (2002) 633-635.
166. Discrete vector spatial solitons in a nonlinear waveguide array, M.J. Ablowitz and Z. Mussli- mani, Phys. Rev. E, 65 (2002) 056618-1-13.
167. Resonant intrachannel pulse interactions in dispersion-managed transmission systems, M.J. Ablowitz and T.Hirooka, IEEE Journal on Selected Topics in Quantum Electronics, 8(2002) 603-615.
168. Higher order asymptotic analysis of dispersion-managed transmission systems: solutions and their characteristics, M.J. Ablowitz, T.Hirooka and T. Inoue, J. Opt. Soc. Am. B - Opt. Phys., 19 (2002) 2876-2885.
169. The Cauchy problem for the Kadomtsev-Petviashili II equation with nondecaying data along a line, J. Villarroel and M.J. Ablowitz, Stud. Appl. Math., 109 (2002) 151-162.
170. Dark and gray strong dispersion-managed solitons, M.J. Ablowitz and Z. Musslimani, Phys. Rev. E, 67 (2003) 025601-1-4.
171. Four-wave mixing in dispersion-managed return-to-zero systems, M.J. Ablowitz, G. Biondini, S. Chakravarty and R.L. Horne, J. Opt. Soc. Am. B - Opt. Phys., 20 (2003) 831-845.
172. On a two-phase free boundary problem, M.J. Ablowitz and S. De Lillo, J. of Phys. A: Math. and Gen., 36 (2003) 4307-4319.
173. Incomplete collisions in strongly dispersion-managed return-to-zero communication systems, M.J. Ablowitz, A. Docherty and T. Hirooka, Opt. Lett., 28 (2003) 1191-1193.
174. Discrete spatial solitons in a diffraction-managed nonlinear waveguide array: a unified ap- proach, M.J. Ablowitz and Z. Musslimani, Physica D - Nonlin. Phenom., 184, (2003) 276-303.
175. On the discrete spectrum of systems in the plane and the Davey-Stewartson II equation, J. Villarroel and M.J. Ablowitz, SIAM J. Math. Anal., 34 (2003) 1253-1278.
176. Integrable systems and reductions of the self-dual Yang-Mills equations, M.J. Ablowitz, S. Chakravarty and R.G. Halburd, J. Math. Phys., 44 (2003) 3147-3173.
177. Dispersion management for randomly varying optical fibers, M.J. Ablowitz and J.T. Moeser, Opt. Lett., 29 (2004) 821-823.
178. Carrier-envelope phase slip of ultrashort dispersion- managed solitons, M.J. Ablowitz, B. Ilan and S. Cundiff, Opt. Lett., 29 (2004) 1808-1810.
179. On the initial value problem for the KPII equation with data that does not decay along a line, J. Villarroel and M.J. Ablowitz, Nonlinearity, 17 (2004) 1843-1866. * in journal article, Ablowitz was incorrectly spelled as “Abowitz”
180. Reduction of collision-induced timing shifts in dispersion-managed quasi-linear systems with periodic group-delay dispersion compensation, M.J. Ablowitz, C. Ahrens, G. Biondini, S. Chakravarty and A.Docherty, Opt. Lett., 29 (2004) 2354-2356.
181. Soliton interactions in the vector NLS equation, M. J. Ablowitz, B. Prinari and A.D. Trubatch, Inverse Prob., 20 (2004) 1217-1237.
182. Integrable nonlinear Schr¨odinger systems and their soliton dynamics, M.J. Ablowitz, B. Prinari and A.D.Trubatch, Dynam. Part. Diff. Eq., 1 (2004) 239-299.
183. Solvability of the direct and inverse problems for the nonlinear Schrodinger equation, J. Villarroel, M.J. Ablowitz and B. Prinari, Acta Applic. Math., 87 (2005) 245-280.
184. Dynamics of nonlinear and dispersion managed solitons, Q. Quraishi, S. Cundiff, B. Ilan and M.J. Ablowitz, Phys. Rev. Lett., 94 (2005) 243904.
185. Spectral renormalization method for computing self-localized solutions to nonlinear systems, M.J. Ablowitz and Z. Musslimani, Opt. Lett., 30 (2005) 2140-2142.
186. On a ”quasi” integrable discrete Eckhaus equation, M.J. Ablowitz, C.D. Ahrens and S. DeLillo, J. of Nonlin. Math. Phys., 12 (2005) 1-12.
187. Wave dynamics in optically modulated waveguide arrays, M.J. Ablowitz, K. Julien, Z. Mus- slimani and M. Weinstein, Phys. Rev. E, 71 (2005) 055602.
188. Periodic-group-delay dispersion compensation reduces collision-induced timing shifts in dispersion-managed quasilinear systems, M.J. Ablowitz, C. Ahrens, G. Biondini, S. Chakravarty and A. Docherty, Theor. and Math. Phys., 144 (2005) 881-887.
189. Calculation, characterization, and application of the time shift function in wavelength-division- multiplexed return-to-zero systems, O.V. Sinkin, V.S. Gregorian, J. Zweck, C.R. Menyuk, A. Docherty and M.J Ablowitz, Opt. Lett., 30 (2005) 2056-2058.
190. Wave collapse in a class of nonlocal nonlinear Schrodinger equations, M.J. Ablowitz, I. Bakirtas and B. Ilan, Physica D - Nonlin. Phenom., 207 (2005) 230-253.
191. Asymptotic analysis of collision-induced timing shifts in return-to-zero quasi-linear sys- tems with pre-dispersion and post-dispersion compensation, C.D. Ahrens, M.J. Ablowitz, A. Docherty, O.V. Sinkin, V.Gregorian and C.R. Menyuk, Opt. Lett., 31 (2006) 5-7.
192. Theory of magnetodynamics induced by spin torque in perpendicularly magnetized thin films, M.A. Hoefer, M.J. Ablowitz, B. Ilan, M.R. Pufall, and T.J. Silva, Phys. Rev. Lett., 95 (2005) 267206.
193. Discrete vector solitons: Composite solitons, YangBaxter maps and computation, M.J. Ablowitz, B. Prinari and A.D. Trubatch, Stud. Appl. Math., 116 (2006) 97-133.
194. Inverse scattering transform for the vector nonlinear Schrodinger equation with nonvanishing boundary conditions, B. Prinari, M.J. Ablowitz and G. Biondini, J. Math. Phys., 47 (2006) 063508-1-33.
195. Noise-induced linewidth in frequency combs, M.J. Ablowitz, B. Ilan and S. Cundiff, Opt. Lett., 31 (2006) 1875-1877.
196. On a new non-local formulation of water waves, M.J. Ablowitz, A.S. Fokas and Z. Musslimani, J. of Fluid Mech., 562 (2006) 313-343.
197. Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal struc- tures, M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, Phys. Rev. E, 74 (2006) 035601.
198. Dispersive and classical shock waves in Bose-Einstein condensates and gas dynamics, M.A. Hoefer, M.J. Ablowitz, I. Coddington, E.A. Cornell, P. Engels and V. Schweikhard, Phys. Rev. A., 74 (2006) 023623.
199. Integrable systems and modular forms of level 2, M.J. Ablowitz, S. Chakravarty and H. Hahn, J. of Phys. A - Math. and Gen., 39 (2006) 15341-15353.
200. Two-dimensional solitons in irregular lattice systems, M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, Theor. Math. Phys., 151 (2007) 723-734.
201. Inverse scattering transform for the integrable discrete nonlinear Schrodinger equation with nonvanishing boundary conditions, M.J. Ablowitz, G. Biondini and B. Prinari, Inverse Prob.,23 (2007) 1711-1758.
202. Interactions of dispersive shock waves, M.A. Hoefer and M.J. Ablowitz, Physica D - Nonlin. Phenom., 236 (2007) 44-64.
203. On a class of nonlocal nonlinear Schrodinger equations and wave collapse, M.J. Ablowitz, I. Birkitas and B. Ilan, Eur. Phys. J.- Spec. Top., 147 (2007) 343-362.
204. Piston dispersive shock wave problem, M.A. Hoefer, M.J. Ablowitz and P. Engels, Phys. Rev. Lett., 100, (2008) 084504.
205. Solitons in dispersion-managed mode-locked lasers, M.J. Ablowitz, T.P. Horikis and B. Ilan, Phys. Rev. A, 77 (2008) 033814.
206. Pulse dynamics and solitons in mode-locked lasers, M.J. Ablowitz and T.P. Horikis, Phys. Rev. A, 78 (2008) 011802.
207. Spectral formulation of the two fluid Euler equations with a free surface and long wave reductions, M.J. Ablowitz and T. S. Haut, Analysis and Applications, 6 (2008) 323-348.
208. Damping of periodic waves in physically significant wave systems, M.J. Ablowitz, S.A. Ablowitz and N. Antar, Stud. Appl. Math. 121 (2008) 313-335.
209. Solitons in optics and water waves, M.J. Ablowitz, Mathematics Today, (April, 2008), 198-200.
210. Asymptotic Analysis of Pulse Dynamics in Mode-locked Lasers, Mark J. Ablowitz, Theodoros P. Horikis, Sean D. Nixon and Yi Zhu, Stud. Appl. Math. 122 (2009) 411-425.
211. Conical Diffraction in Honeycomb lattices, Mark J. Ablowitz, Sean D. Nixon and Yi Zhu, Physical Review A, 79 (2009) 053830
212. Soliton Generation and Multiple Phases in Dispersive Shock and Rarefaction Wave Interaction, M. J. Ablowitz, D.E. Baldwin, and M. A. Hoefer, Physical Review E, 80 (2009) 016603
213. Solitons and spectral renormalization methods in nonlinear optics, M. J. Ablowitz and T. P. Horikis, Eur. Phys. J. Special Topics 173 (2009) 147-166.
214. Solitons in normally dispersive mode-locked lasers, M.J. Ablowitz and T.P. Horikis, Physical Review A 79 (2009) 063845.
215. A reformulation and applications of interfacial fluids with a free surface, T.S. Haut and M.J. Ablowitz, J. Fl. Mech. 631 (2009) 375-396.
216. Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions, M.J. Ablowitz and T.S. Haut, Proc. Roy. Soc. A 465 (2009) 2725-2749
217. Soliton strings and interactions in mode-locked lasers, Mark J. Ablowitz, Theodoros P. Horikis and Sean D. Nixon Opt. Commun.282 (2009) 4127-4135.
218. Coupled nonlinear Schr¨odinger equations from interfacial fluids with a free surface, M.J. Ablowitz and T.S. Haut, Theor. Math. Phys. 159 (2009) 689-697.
219. Nonlinear waves in optical media, Mark J. Ablowitz, Theodoros P. Horikis, Journal of Com- putational and Applied Mathematics 234 (2010) 1896-1903.
220. Band Gap Boundaries and Fundamental Solitons in Complex 2D Nonlinear Lattices, M.J. Ablowitz, N. Antar, I. Bakirtas and B. Ilan, Physical Review A, 81 (2010) 033834.
221. Parameterizations of the Chazy Equation, S. Chakravarty and M. J. Ablowitz, Stud. in Appl. Math., 124, (2010) 105-135.
222. Asymptotic expansions for large amplitude solitary gravity-capillary waves, M.J. Ablowitz and T.S. Haut, J. Phys. Math and Theoretical, 43 (2010) 434005.
223. Evolution of Bloch-mode-envelopes in two-dimensional generalized honeycomb lattices, Mark J. Ablowitz, and Yi Zhu, Physical Review A 82 (2010) 013840.
224. Perturbations of dark solitons, M. J. Ablowitz, S. D. Nixon, T. P. Horikis and D. J. Frantzeskakis, Proc. Roy. Soc. A 467 (2011) 2597-2621.
*225. Nonlinear wave dynamics: from lasers to fluids, Mark J. Ablowitz, Terry S. Haut, Theodoros P. Horikis, Sean D. Nixon and Yi Zhu, Discrete and Continuous Dynamical Systems, Series S 4 (2011) 923-955
226. Dark solitons in mode-locked lasers, M. J. Ablowitz, T. P. Horikis, S. D. Nixon, and D. J. Frantzeskakis, Opt. Lett. 36 (2011) 793-795
227. On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation, M. J. Ablowitz and W. C. Curtis, J. Phys. A-Math and Theor. 44 (2011) 195202
228. Nonlinear diffraction in photonic graphene, Mark J. Ablowitz, and Yi Zhu, Optics Letters 36 (2011) 3762-3764
229. Nonlinear waves in shallow honeycomb lattices, M. J. Ablowitz and Yi Zhu, SIAM J. on Appl. Math.,72, (2012) 240-260
230. Vortex and dipole solitons in complex 2D nonlinear lattices, M. J. Ablowitz, N. Antar, I. Bakirtas and B. Ilan, Phys. Rev. A, . 86, (2012) 033804
231. **Nonlinear shallow ocean-wave soliton interactions on flat beaches, M. J. Ablowitz and D. E. Baldwin, Phys. Rev. E, . 86 036305 (2012)
232. On tight-binding approximations in optical lattices, M.J. Ablowitz, Mark J., C.W. Curtis, Y. Zhu, Stud. Appl. Math.,129, (2012) 362-388
233. Traveling waves in elastic rods with arbitrary curvature and torsion, M. J. Ablowitz, V. Barone, S. De Lillo and M. Sommacal, J. Nonlinear Sci.22 (2012), 1013-1040
234. Unified Orbital Description of the Envelope Dynamics in Two-Dimensional Simple Periodic Lattices, M.J. Ablowitz and Y. Zhu, Stud. Appl. Math, 131 (2013) 41-71
235. Integrable nonlocal nonlinear Schrodinger equation, M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 110 (2013) 064105
236. Interactions and asymptotics of dispersive shock waves - Korteweg-de Vries Equation, M. J. Ablowitz and D. E. Baldwin, Phys Lett. A, 377 (2013) 555-559
237. Dark solitons of the power-energy saturation model: application to mode-locked lasers, M. J. Ablowitz, T. P. Horikis, S. D. Nixon, and D. J. Frantzeskakis, J. of Phys. A: Math. Theor. 46 (2013) 095201
238. Dispersive shock wave interactions and asymptotics, M. J. Ablowitz and D. E. Baldwin, Phys. Rev. E., 87 (2013) 022906
239. Conservation Laws and nondecaying-solutions for the Benney-Luke equation, M.J. Ablowitz and C.W. Curtis, Proc. R. Soc. A, 469, (2013) 201206
240. Localized nonlinear edge states in honeycomb lattices, M.J. Ablowitz and C.W. Curtis, 88 Phys. Rev. A (2013) 013850
241. Nonlinear wave packets in deformed honeycomb lattices, M.J. Ablowitz and Y. Zhu, SIAM J. Appl. Math. 87 (2013) 19591979
242. On the Existence of Real Spectra in PT-Symmetric Honeycomb Optical Lattices, C. W. Curtis and M. J. Ablowitz J. of Phys. A: Math. Theor. 47 (2014) 225205
243. Nonlinear Temporal-Spatial Surface Plasmon Polaritons, M. J. Ablowitz and S. T. J. Butler Optics Commun 330 (2014) 49-55
244. Inverse scattering transform for 3-level coupled Maxwell Bloch equations with inhomogeneous broadening, S Chakravarty, B Prinari, MJ Ablowitz, Physica D: Nonlinear Phenomena 278, (2014) 58-78
245. Linear and nonlinear traveling edge waves in optical honeycomb lattices MJ Ablowitz, CW Curtis and YP Ma Physical Review A 90 (2014) 023813
246. Passive mode-locking under higher order effects, T.P. Horikis and M.J. Ablowitz, J. Opt. Soc. Am. B 31 (2014) 2748-2753
247. Integrable discrete PT symmetric model, M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. E 90 (2014) 032912
248. Interacting nonlinear wave envelopes and rogue wave formation in deep water, Mark J. Ablowitz and Theodoros P. Horikis, {\it Phys. Fluids} {\bf 27} (2015) 012107, DOI. http://dx.doi.org/10.1063/1.4906770
249. Unveiling pseudospin and angular momentum in photonic graphene, D. Song, V. Paltoglou, S. Liu, Y. Zhu, D. Gallardo, L. Tang, J. Xu, M. Ablowitz, N. Efremidis and Zhigang Chen, {\it Nature Commun.}, {\bf 6} (2015) DOI: 10.1038
250. Adiabatic dynamics of edge waves in photonic graphene, MJ Ablowitz, CW Curtis and YP Ma, {\it 2D Materials} {\bf XX} (2015)
Articles denoted by * are not contained in web of knowledge data base.
**This article plus photos/videos taken in Nuevo Vallarta, Mexico by MJA and Venice Beach, CA, by DEB, was featured on the American Physical Society (APS) web site: APS synopsis; subsequently it was identified fora special focus article in Physics Today–November issue. It also was featured by the American Meteorological Society (Bulletin January.–2013) and was picked up by science news services: ‘OurAmazingPlanet’–syndicatedby many news organizations; New Scientist; NRC Handelsblad: the largest evening newspaper in Netherlands; NBC.com; National (U.S.A.) Tsunami Hazard Mitigation Program, plus others... SIAM News requested we write an article appropriate for applied mathematicians This was subsequently published in the June, 2013 issue of SIAM News.