Abstract for Olga Trichtchenko

Olga Trichtchenko (Western University)

Thursday, March 30, 2023

Travelling wave solutions to nonlinear dispersive equations describing water waves

Abstract: In this work, we examine periodic travelling wave solutions to weakly nonlinear dispersive equations such as KdV and Kawahara, which model water waves. In particular, we compare and contrast how solutions depend on the linear operator and what conditions need to be met for resonances to arise. In examining stability of these travelling waves, we show how instabilities can arise and how they can be predicted by the dispersion relation.