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Exact Solutions and Symmetry Analysis of a Boussinesq Type Equation for Longitudinal Waves Through a Magneto-Electro-Elastic Circular Rod

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Abstract

In this work the longitudinal wave equation through magneto-electro-elastic circular rod is studied analytically. Painlevé test is performed to check integrability of the equation. Exact solitary wave solutions are found by homogeneous balance method and Tanh method and are plotted using suitable values of physical parameters. A solution similar to an earlier related work (Xue et al. in Smart Mater Struct 20:105010, 2011; Ma et al. in Int J Comput Sci Issues 10 (1): 62–68, 2013) is obtained. However a new solution is obtained as well. Lie symmetry analysis has been done and similarity reduction of the equation is presented. Dependence of the solution on the longitudinal wave velocity and the dispersion parameter related to the transverse Poisson effect are obtained numerically. Numerical results related to phase velocity etc for different materials have been derived and compared.

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Acknowledgements

Arindam Ghosh is grateful to MHRD India for their financial support.

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Authors and Affiliations

  1. Department of Mathematics, NIT Durgapur, Durgapur, India

    Arindam Ghosh & Sarit Maitra

  2. Department of Physics, Jadavpur University, Kolkata, India

    Asesh Roy Chowdhury

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  1. Arindam Ghosh
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  2. Sarit Maitra
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Correspondence to Arindam Ghosh.

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Ghosh, A., Maitra, S. & Chowdhury, A.R. Exact Solutions and Symmetry Analysis of a Boussinesq Type Equation for Longitudinal Waves Through a Magneto-Electro-Elastic Circular Rod. Int. J. Appl. Comput. Math 7, 171 (2021). https://doi.org/10.1007/s40819-021-01105-3

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