Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 194329, 14 pages
doi:10.1155/2010/194329
Research Article

Application of the Cole-Hopf Transformation for Finding Exact Solutions to Several Forms of the Seventh-Order KdV Equation

Alvaro H. Salas1,2 and Cesar A. Gómez S.3

1Department of Mathematics, University of Caldas, Manizales Cll 65 # 26-10, A.A. 275, Colombia
2Department of Mathematics, National University of Colombia, Campus La Nubia, Manizales, Caldas, Colombia
3Department of Mathematics, National University of Colombia, Bogotá Cll 45, Cra 30, Colombia

Received 20 August 2009; Revised 5 November 2009; Accepted 28 January 2010

Academic Editor: Gradimir V. Milovanović

Copyright © 2010 Alvaro H. Salas and Cesar A. Gómez S. 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

We use a generalized Cole-Hopf transformation to obtain a condition that allows us to find exact solutions for several forms of the general seventh-order KdV equation (KdV7). A remarkable fact is that this condition is satisfied by three well-known particular cases of the KdV7. We also show some solutions in these cases. In the particular case of the seventh-order Kaup-Kupershmidt KdV equation we obtain other solutions by some ansatzes different from the Cole-Hopf transformation.