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The auxiliary elliptic-like equation and the exp-function method

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Abstract

The auxiliary equation method is very useful for finding the exact solutions of the nonlinear evolution equations. In this paper, a new idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the auxiliary elliptic-like equation are derived using exp-function method, and then the exact solutions of the nonlinear evolution equations are derived with the aid of auxiliary elliptic-like equation. As examples, the RKL models, the high-order nonlinear Schrödinger equation, the Hamilton amplitude equation, the generalized Hirota-Satsuma coupled KdV system and the generalized ZK-BBM equation are investigated and the exact solutions are presented using this method.

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Authors and Affiliations

  1. College of Science, Zhongyuan University of Technology, Zhengzhou, 450007, China

    Hong Li

  2. College of Science, Henan University of Science and Technology, Luoyang, 471003, China

    Jin-Liang Zhang

Authors
  1. Hong Li
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  2. Jin-Liang Zhang
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Correspondence to Jin-Liang Zhang.

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Li, H., Zhang, JL. The auxiliary elliptic-like equation and the exp-function method. Pramana - J Phys 72, 915–925 (2009). https://doi.org/10.1007/s12043-009-0085-9

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  • DOI: https://doi.org/10.1007/s12043-009-0085-9

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