Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 872385, 10 pages
http://dx.doi.org/10.1155/2012/872385
Research Article

The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source

Yali Shen, Fengqin Zhang, and Xiaomei Feng

Department of Mathematics, Yuncheng University, Yuncheng 044000, China

Received 31 October 2011; Accepted 27 February 2012

Academic Editor: Beatrice Paternoster

Copyright © 2012 Yali Shen et al. 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

The Painlevé property and Bäcklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property. In order to further prove its integrality, we give its bilinear form and construct its bilinear Bäcklund transformation by the Hirota's bilinear operator. And then the soliton solution of the equation is obtained, based on the proposed bilinear form.