Multi-pulse solitary waves in Hamiltonian systems

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 multi-pulses in three Hamiltonian systems: the discrete nonlinear Schrodinger equation, a fourth-order suspension bridge model, and the fifth order Korteweg-de Vries equation. We will show that for all three equations, multi-pulses solutions exist, but they must obey geometric constraints imposed by the system. The spectral stability of these solutions depends completely on the geometry of the multi-pulse.

Date
Sep 24, 2020
Location
SMU math colloquium
Dallas, TX (virtual)
Ross Parker
Ross Parker
RTG postdoctoral fellow

I am a postdoctoral fellow in the department of mathematics at Southern Methodist University.