Traveling wave solution of the Kuramoto-Sivashinsky equation : a computational study

Abstract

This work considers the numerical solution of the Kuramoto-Sivashinsky equation using the fractional time splitting method. We will investigate the numerical behavior of two categories of the traveling wave solutions documented in the literature (Hooper & Grimshaw (1998)), namely: the regular shocks and the oscillatory shocks. We will also illustrate the ability of the scheme to produce convergent chaotic solutions.