Multi-pulse solitary waves in Hamiltonian systems: theory and numerics

Abstract

Solitary waves, localized disturbances that maintain their shape as they propagate at a constant velocity, have been an object of mathematical and experimental interest for over a century, and have applications in diverse fields such as fluid mechanics, nonlinear optics, and molecular systems. Multi-pulses are multi-modal solitary waves which resemble multiple, well-separated copies of a single solitary wave. In this talk, we will look at the existence and stability of multi-pulses in one continuous system, the 5th order Korteweg-de Vries equation, and one discrete system, the discrete nonlinear Schrodinger equation. We will discuss how these solutions are constructed analytically using a spatial dynamics approach, as well as how we can generate them numerically using techniques such as parameter continuation.

Ross Parker

RTG postdoctoral fellow / visiting assistant professor

I am a postdoctoral fellow and visiting assistant professor in the department of mathematics at Southern Methodist University.