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Integrable system modelling shallow water waves: Kaup–Boussinesq shallow water system

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Abstract

Extended F-expansion method is proposed to seek exact solutions of the integrable nonlinear Kaup–Boussinesq shallow water system, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the extended F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously a number of periodic wave solutions expressed by various Jacobi elliptic functions for the integrable nonlinear Kaup-Boussinesq shallow water system. In the limiting cases, the solitary wave solutions are obtained as well.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    A. H. Bhrawy & M. M. Tharwat

  2. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    A. H. Bhrawy, M. M. Tharwat & M. A. Abdelkawy

Authors
  1. A. H. Bhrawy
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  2. M. M. Tharwat
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  3. M. A. Abdelkawy
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Correspondence to M. A. Abdelkawy.

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Bhrawy, A.H., Tharwat, M.M. & Abdelkawy, M.A. Integrable system modelling shallow water waves: Kaup–Boussinesq shallow water system. Indian J Phys 87, 665–671 (2013). https://doi.org/10.1007/s12648-013-0260-1

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  • DOI: https://doi.org/10.1007/s12648-013-0260-1

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