Nonlinear Waves Seminar

Topologically Protected Edge Modes in Longitudinally Driven Waveguides A tight-binding approximation is developed for deep longitudinally driven photonic lattices. The physical system considered is that of a laser-etched waveguide array which is helically-varying in the direction of propagation. Focus is placed on the so-called Lieb and Kagome lattices. The lattice...

Soliton fission from a large disturbance in the viscous fluid conduit system The resolution of a large, localized initial disturbance is considered in the context of the viscous fluid conduit system--the driven, cylindrical, free interface between two miscible Stokes fluids with high viscosity contrast. Due to buoyancy induced nonlinear self-steepening...

Quantum Turbulent Structure in Light The infinite superpositions of random plane waves are known to be threaded with vortex line singularities which form complicated tangles and obey strict topological rules. We observe that within these structures a timelike axis appears to emerge with which we can define vortex velocities in...

Computing traveling wave solutions of the fifth order Korteweg-de Vries equation through Whitham theory Whitham modulation theory is a useful tool for describing the adiabatic evolution of periodic solutions to nonlinear dispersive equations. Modulation theory yields a first order system of quasilinear partial differential equations which describe the evolution of...

Nonlinear waves in rotating fluids In this presentation the non-trivial dynamics of nonlinear dispersive waves affected by the Coriolis force is discussed. Applications include surface and internal waves in the ocean, magnetic sound in plasma, and other phenomena. The corresponding model equation (rKdV equation) derived by the author has the...

Geometric Quantum Hydrodynamics and the Evolution of Vortex Lines he simplest manifestation of a circulatory field occurs when a vortex line breaks the simple connectivity of an otherwise irrotational fluid. Arnold's program tells us that the evolution of such a vortex is Hamiltonian with respect to the arclength. The simplest...

A path from fractional Schrödinger equation to design and discovery of novel quantum materials Transport phenomena in multi-scale classical systems, such as disordered media, porous materials, and turbulent fluids, are characterized by multiple spatial and temporal scales, nonlocality, fractional geometry, and non-Gaussian statistics. Transport in multi-scale classical materials is described...

Rapid soliton nucleation and dynamics in magnetic materials Magnetism in solid materials is a fascinating yet complex phenomenon that encompasses vastly different length and time scales. This complexity is typically resolved by establishing equations that are valid at different scales. For example, magnetic dynamics at the atomic level can be...

Prediction of random and chaotic dynamics in nonlinear optics The control and prediction of interactions between high-power, nonlinear laser beams is a longstanding open problem in optics and mathematics. One of the traditional underlying assumptions in this field has been that these dynamics are governed by a deterministic model. Lately,...

Rational solutions of three integrable equations and applications to rogue waves In this talk I shall discuss rational solutions of three integrable equations, the Boussinesq equation, the focusing nonlinear Schrödinger (NLS) equation and the Kadomtsev-Petviashvili I (KPI) equation. The Boussinesq equation was introduced by Boussinesq in 1871 to describe the...