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


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.

Apr 8, 2022
UT Dallas computational science seminar
Ross Parker
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.