• Invariance analysis, optimal system and conservation laws of $(2 + 1)$-dimensional non-linear Vakhnenko equation

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/095/0008

    • Keywords

       

      Vakhnenko equation; Lie group of transformation; infinitesimal generator; adjoint equations; optimal system; conservation laws; invariant solutions.

    • Abstract

       

      In this article, we study a $(2 + 1)$-dimensional non-linear Vakhnenko equation which appears in a relaxing high rate active barothropic medium. The Lie symmetry analysis is applied to study the solution of $(2+1)$-dimensional Vakhnenko equation and also used to find the optimal system of one-dimensional Lie subalgebra. The two-dimensional non-linear Vakhnenko equation is reduced to various ordinary differential equations by applying similarity transformation method, and solving these reduced ordinary differential equations, we find invariant solutions of $(2 + 1)$-dimensional Vakhnenko equation. Moreover, the adjoint equation of the Vakhnenko equation and its conservation laws are also obtained, which can be used for mathematical analysis.

    • Author Affiliations

       

      SHALINI YADAV1 ASTHA CHAUHAN1 RAJAN ARORA1

      1. Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee 247 667, India
    • Dates

       
  • Pramana – Journal of Physics | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.