International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 61-64, Pages 3369-3377
doi:10.1155/S0161171204408552

Bäcklund transformations for several cases of a type of generalized KdV equation

Abstract

An alternate generalized Korteweg-de Vries system is studied here. A procedure for generating solutions is given. A theorem is presented, which is subsequently applied to this equation to obtain a type of Bäcklund transformation for several specific cases of the power of the derivative term appearing in the equation. In the process, several interesting, new, ordinary, differential equations are generated and studied.