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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

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

Quantum Turbulent Structure in LightThe 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

Computing traveling wave solutions of the fifth order Korteweg-de Vries equation through Whitham theoryWhitham modulation theory is a useful tool for describing the adiabatic evolution of periodic solutions to nonlinear dispersive equations.

Nonlinear waves in rotating fluidsIn 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

Geometric Quantum Hydrodynamics and the Evolution of Vortex Lineshe 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

A path from fractional Schrödinger equation to design and discovery of novel quantum materialsTransport phenomena in multi-scale classical systems, such as disordered media, porous materials, and turbulent fluids, are characterized by multiple

Rapid soliton nucleation and dynamics in magnetic materialsMagnetism 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

Prediction of random and chaotic dynamics in nonlinear opticsThe 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

Rational solutions of three integrable equations and applications to rogue wavesIn this talk I shall discuss rational solutions of three integrable equations, the Boussinesq equation, the focusing nonlinear Schrödinger (NLS) equation and the