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Solitons and other nonlinear waves of the Boussinesq equation

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Abstract

This paper studies the dynamics of shallow water waves that are governed by the Boussinesq equations. A few perturbation terms are taken into account. The ansatz method is used to carry out the perturbed Boussinesq equation. Later on, the mapping method is used to extract a few more analytical solutions. Additionally, the Weierstrass elliptic function method is also used to obtain solitary waves and singular soliton solutions. Finally, the Lie symmetry approach is used to extract a few more additional solutions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al Khod 123, Muscat, Oman

    E. V. Krishnan

  2. School of Mathematics and Computer Applications, Thapar University, Patiala, 147004, Punjab, India

    Sachin Kumar

  3. Department of Mathematical Sciences, Delaware State University, Dover, DE, 19901-2277, USA

    Anjan Biswas

Authors
  1. E. V. Krishnan
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  2. Sachin Kumar
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  3. Anjan Biswas
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Correspondence to Anjan Biswas.

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Krishnan, E.V., Kumar, S. & Biswas, A. Solitons and other nonlinear waves of the Boussinesq equation. Nonlinear Dyn 70, 1213–1221 (2012). https://doi.org/10.1007/s11071-012-0525-9

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  • DOI: https://doi.org/10.1007/s11071-012-0525-9

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