Stochastic amplitude modulation of nonlinear dispersive waves

Abstract

This dissertation investigates the propagation of solitary waves in the presence of random disturbances. We focus on paradigm models from nonlinear dispersive wave theory: the Korteweg–de Vries equation and the Fermi–Pasta–Ulam–Tsingou system. In both cases, random disturbances influence the wave amplitude. We develop a framework to track the evolution of the wave amplitude, yielding explicit predictions for its behavior, which we validate through numerical simulations. These results are supported by a rigorous analysis of wave stability.