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Exact solutions of some general nonlinear wave equations in elasticity

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Abstract

A similarity analysis of a nonlinear wave equation in elasticity is studied; in particular, one with anharmonic corrections. The symmetry transformation give rise to exact solutions via the method of invariants. In some cases, graphical figure of the solutions are presented. Furthermore, we consider some cases wherein the velocities of the longitudinal and transversal plane waves are variable. Finally, a brief discussion on how a symmetry analysis on a perturbation of the elasticity equation can be pursued.

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Authors and Affiliations

  1. Department of Mathematical Science, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    A. H. Bokhari & F. D. Zaman

  2. School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

    A. H. Kara

Authors
  1. A. H. Bokhari
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  2. A. H. Kara
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  3. F. D. Zaman
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Correspondence to A. H. Kara.

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Bokhari, A.H., Kara, A.H. & Zaman, F.D. Exact solutions of some general nonlinear wave equations in elasticity. Nonlinear Dyn 48, 49–54 (2007). https://doi.org/10.1007/s11071-006-9050-z

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  • DOI: https://doi.org/10.1007/s11071-006-9050-z

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