A Bäcklund Transformation for a Higher Order Korteweg-De Vries Equation

Abstract

A Bäcklund transformation in bilinear forms is presented for a higher order Korteweg-de Vries equation, which is a natural extension of the Korteweg-de Vries equation written in a bilinear form. The Bäcklund transformation in ordinary forms and the inverse scattering scheme are given for this higher order equation. Also, the first eleven of the infinity of conservation quantities for this equation are derived from the Bäcklung transformation.