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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 63, Pages 3369-3377
http://dx.doi.org/10.1155/S0161171204408552

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

Department of Mathematics, University of Texas, Edinburg 78541-2999, TX, USA

Received 4 August 2004

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.