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

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      https://www.ias.ac.in/article/fulltext/pram/072/06/0915-0925

    • Keywords

       

      Auxiliary equation method; exp-function method; exact solution; RKL models; high-order nonlinear Schrödinger equation; Hamilton amplitude equation; generalized Hirota–Satsuma coupled KdV system; generalized ZK–BBM equation.

    • 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.

    • Author Affiliations

       

      Hong Li1 Jin-Liang Zhang2

      1. College of Science, Zhongyuan University of Technology, Zhengzhou, 450007, China
      2. College of Science, Henan University of Science and Technology, Luoyang, 471003, China
    • Dates

       
  • Pramana – Journal of Physics | News

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