On the Integrability and Exact Solutions of a Generalized Korteweg-de-Vries Equation

Abstract

In Plasma physics, nonlinear ion acoustic waves are shown to be described by the Korteweg-de-Vries equation. When the drag force acted by the waves on the particles is taken into consideration, the governing equation is shown to be a generalized Korteweg-de-Vries equation. The Integrability properties of this equation are discussed. Some exact solutions for this equation are derived by using the techniques of auto-Bäcklund transformation and polynomial invariants.