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Lie symmetries and dynamics of exact solutions of dissipative Zabolotskaya–Khokhlov equation in nonlinear acoustics

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Abstract

This study deals with symmetry reductions and invariant solutions of (2+1)-dimensional dissipative Zabolotskaya–Khokhlov equation. The equation governs the diffraction of sound beam propagation and describes nonlinear effects in stratified media with dissipation. The possible infinitesimal generators and commutative relation are obtained by means of the similarity transformations method. The method is based on invariance property of Lie groups, which results into the reduction in independent variables by one. Thus, twice reductions of Zabolotskaya–Khokhlov equation provide overdetermined equations, which lead to the invariant solutions under some limiting conditions. The obtained solutions are significant to explain diverse physical structures depending upon existing arbitrary functions and constants. In order to get precise insights, the numerical simulation is performed to the obtained solutions. Eventually, kink wave, parabolic, soliton and stationary profiles of the solutions are obtained.

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Authors and Affiliations

  1. Department of Mathematics, Graphic Era University, Dehradun, 248002, India

    Dig Vijay Tanwar

  2. Department of Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

    Abdul–Majid Wazwaz

Authors
  1. Dig Vijay Tanwar
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  2. Abdul–Majid Wazwaz
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Correspondence to Dig Vijay Tanwar.

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Tanwar, D.V., Wazwaz, A. Lie symmetries and dynamics of exact solutions of dissipative Zabolotskaya–Khokhlov equation in nonlinear acoustics. Eur. Phys. J. Plus 135, 520 (2020). https://doi.org/10.1140/epjp/s13360-020-00527-0

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00527-0

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