Traveling waves for a dissipative modified KdV equation

Abstract

In this paper we consider a dispersive–dissipative nonlinear equation which can be regarded as a dissipation perturbed modified KdV equation, governing the evolution of long waves in an elastic rod immersed inside a viscoelastic medium. Using geometric singular perturbation theory, a construction of traveling waves for the equation is shown. This also is illustrated by presenting some numerical calculations.

Keywords

• Perturbed modified KdV equation
• Singular perturbations
• Traveling waves