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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 185469, 11 pages
http://dx.doi.org/10.5402/2012/185469
Research Article

Exact Periodic Solutions of the Nonintegrable Kawahara Equation

Department of Applied Mathematics and Informatics, Technical University of Sofia, P.O. Box 384, 1000 Sofia, Bulgaria

Received 26 April 2012; Accepted 19 July 2012

Academic Editors: M. Ehrnström, K. S. Fa, D. Gepner, and W.-H. Steeb

Copyright © 2012 Ognyan Yordanov Kamenov and Anna P. Angova. 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

In the present paper, we have obtained an exact biperiodic, one-phase solution of the Kawahara evolution equation. Two classes of real periodic waves generated by the biperiodic solution have been analyzed. A modification of the bilinear-transformation method has been applied allowing to provide a single solution of the residual equation derived from the bidifferential reduction of the considered nonintegrable equation. It is shown that the spatial displacements are individual for each separate harmonic of the real periodic solutions.