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

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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.

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Authors and Affiliations

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

    Shalini Yadav, Astha Chauhan & Rajan Arora

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  1. Shalini Yadav
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  2. Astha Chauhan
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  3. Rajan Arora
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Correspondence to Rajan Arora.

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Yadav, S., Chauhan, A. & Arora, R. Invariance analysis, optimal system and conservation laws of \((2+1)\)-dimensional non-linear Vakhnenko equation. Pramana - J Phys 95, 8 (2021). https://doi.org/10.1007/s12043-020-02059-9

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  • DOI: https://doi.org/10.1007/s12043-020-02059-9

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