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Abstract and Applied Analysis
Volume 2013, Article ID 582532, 9 pages
http://dx.doi.org/10.1155/2013/582532
Research Article

Infinitely Many Elliptic Solutions to a Simple Equation and Applications

Institute of Applied Mathematics and Engineering Computations, Hangzhou Dianzi University, Zhejiang, Hangzhou 310018, China

Received 4 June 2013; Accepted 4 July 2013

Academic Editor: Pavel Kurasov

Copyright © 2013 Long Wei and Yang Wang. 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

Based on auxiliary equation method and Bäcklund transformations, we present an idea to find infinitely many Weierstrass and Jacobi elliptic function solutions to some nonlinear problems. First, we give some nonlinear iterated formulae of solutions and some elliptic function solutions to a simple auxiliary equation, which results in infinitely many Weierstrass and Jacobi elliptic function solutions of the simple equation. Then applying auxiliary equation method to some nonlinear problems and combining the results with exact solutions of the auxiliary equation, we obtain infinitely many elliptic function solutions to the corresponding nonlinear problems. The employed approach is powerful and can be also applied to solve other nonlinear differential equations.