Existence of Solitary Waves and Periodic Waves to a Perturbed Generalized KdV Equation

Abstract

In this paper, the existence of solitary waves and periodic waves to a perturbed generalized KdV equation is established by applying the geometric singular perturbation theory and the regular perturbation analysis for a Hamiltonian system. Moreover, upper and lower bounds of the limit wave speed are obtained. Some previous results are extended.

Keywords:

• perturbed generalized KdV equation
• traveling waves
• geometric singular perturbation theory
• regular perturbation analysis for a Hamiltonian system

AMS Subject Classification:

• 34F10
• 35B10
• 35B44
• 35C07