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A study of shallow water waves with Gardner’s equation

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Abstract

In this paper the dynamics of solitary waves governed by Gardner’s equation for shallow water waves is studied. The mapping method is employed to carry out the integration of the equation. Subsequently, the perturbed Gardner equation is studied, and the fixed point of the soliton width is obtained. This fixed point is then classified. The integration of the perturbed Gardner equation is also carried out with the aid of He’s semi-inverse variational principle. Finally, Gardner’s equation with full nonlinearity is solved with the aid of the solitary wave ansatz method.

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Authors and Affiliations

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

    E. V. Krishnan

  2. Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P.O. Box 12, 2300, Annaba, Algeria

    Houria Triki

  3. Laboratory of Engineering Mathematics, Tunisia Polytechnic School, University of 7th November at Carthage, BP 743, La Marsa, 2070, Tunisia

    Manel Labidi

  4. Department of Mathematical Sciences, Center for Research and Education in Optical Sciences and Applications, Delaware State University, Dover, DE, 19901-2277, USA

    Anjan Biswas

Authors
  1. E. V. Krishnan
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  2. Houria Triki
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  3. Manel Labidi
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  4. Anjan Biswas
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Correspondence to Anjan Biswas.

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Krishnan, E.V., Triki, H., Labidi, M. et al. A study of shallow water waves with Gardner’s equation. Nonlinear Dyn 66, 497–507 (2011). https://doi.org/10.1007/s11071-010-9928-7

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  • DOI: https://doi.org/10.1007/s11071-010-9928-7

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