Bäcklund transformation, auto-Bäcklund transformation and exact solutions for KdV-type equations

In plasma physics, fluid dynamics and nonlinear optics, Korteweg-de Vries (KdV)-type equations are used to describe certain phenomena (ion acoustic wave in plasma, quantum hydrodynamic model, wave motion on the surface of shallow water and the unidirectional propagation of long wave of small amplitude and exists in many physical branches). In this paper, KdV-type equations are investigated. We are used Bäcklund Transformation to obtain new exact solutions for the (KdV)-type equations. The method of characteristics is used and the Bäcklund transformation are employed to generate new solutions from the old ones. By the homogenous balance method, we derive an auto–Bäcklund Transformation (ABT) for the KdV equation. Thus, families of solution for KdV-type equations are obtained. Keywords : KdV-type equations B ä cklund transformation, auto- B ä cklund transformation and exact solutions.