Collision dynamics of fronts in the Korteweg-de Vries-Burgers equation

Abstract

Collisions between propagating fronts in the Korteweg-de Vries-Burgers equation are investigated. It is shown that this simple model, which incorporates non-linearity, damping and dispersion, possesses propagating fronts whose structure and dynamics yields to a detailed analysis. The propagating fronts are related to those of the Fisher equation. The binary collision process is examined in some detail: A model for the variations of the front velocity that occur during the collision event is presented. The model results are compared with simulations. Random initial conditions that produce multiple fronts are also studied and the long-time dynamics is described in terms of a sequence of binary coalescence events.