Existence and Uniqueness of Periodic and Solitary Waves for a Perturbed Generalized KdV Equation

Abstract

This paper establishes the existence and uniqueness of periodic and solitary waves for a perturbed generalized KdV equation. We prove that the periodic wave persists when the wave speed is in a certain interval, and the wavelength of the periodic wave is an increasing function. Furthermore, under the condition of the unique periodic wave exists, the interval of wave speed $c$ becomes smaller as the power $n$ increases.