Existence of Traveling Wave Fronts for a Generalized KdV–mKdV Equation

Abstract

This paper deals with the existence of traveling wave fronts for a generalized KdV–mKdV equation. We first establish the existence of traveling wave solutions for the equation without delay, and then we prove the existence of traveling wave fronts for the equation with a special local delay convolution kernel and a special nonlocal delay convolution kernel by using geometric singular perturbation theory, Fredholm theory and the linear chain trick.

Keywords:

• KdV–mKdV equation
• traveling wave solution
• geometric singular perturbation
• linear chain trick

AMS Subject Classification:

• 35Q53