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    • Lie point symmetries, conservation laws and exact solutions of (1 + n)-dimensional modified Zakharov–Kuznetsov equation describing the waves in plasma physics

      MUHAMMAD NASIR ALI ALY R SEADAWY SYED MUHAMMAD HUSNINE

      Research Article Volume 91 Issue 4 October 2018 Article ID 0048

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/091/04/0048

    • Keywords

       

      Modified Zakharov–Kuznetsov equation; formal Lagrangian; nonlinear self-adjointness; conservation laws; modified Kudryshov method; solitary wave ansatz method; $(G'/G)$-expansion method

    • Abstract

       

      In this study, we explore the modified form of (1 + n)-dimensional Zakharov–Kuznetsov equation, which is used to investigate the waves in dusty and magnetised plasma. It is proved that the equation follows the property of nonlinear self-adjointness. Lie point symmetries are calculated and conservation laws in the framework of the new general conservation theorem of Ibragimov are obtained. The $(1/G'), (G'/G)$-expansion and modified Kudryshov methods are applied to extract exact analytical solutions. The so-called bright, dark and singular solutions are also found using the solitary wave ansatz method. The results obtained in this study are new and may be of significant importance where this model is used to study the waves in different plasmas.

    • Author Affiliations

       

      MUHAMMAD NASIR ALI1 ALY R SEADAWY SYED MUHAMMAD HUSNINE1

      1. Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore 54000, Pakistan

    • Dates

       
      Published
      1 October 2018
      Manuscript received
      28 November 2017
      Manuscript revised
      26 February 2018
      Accepted
      27 February 2018
      Early published
      Unedited version published online
      Final version published online
      10 August 2018

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