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    • Solitary wave solution to a singularly perturbed generalized Gardner equation with nonlinear terms of any order

      J B ZHOU J XU J D WEI X Q YANG

      Research Article Volume 88 Issue 4 April 2017 Article ID 0069

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/088/04/0069

    • Keywords

       

      Perturbed generalized Gardner equation; solitary wave solution; geometric singular perturbation theory

    • Abstract

       

      This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis.

    • Author Affiliations

       

      J B ZHOU1 J XU1 J D WEI1 X Q YANG1

      1. Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, People’s Republic of China

    • Dates

       
      Published
      16 April 2017
      Manuscript received
      22 July 2016
      Manuscript revised
      7 October 2016
      Accepted
      27 October 2016
      Early published
      Unedited version published online
      Final version published online
      24 March 2017

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