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The nonlinear dispersive Davey-Stewartson system for surface waves propagation in shallow water and its stability

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Abstract.

The three-dimensional (3-D) nonlinear and dispersive PDEs system for surface waves propagating at undisturbed water surface under the gravity force and surface tension effects are studied. By applying the reductive perturbation method, we derive the (2 + 1) -dimensions form of the Davey-Stewartson (DS) system for the modulation of 2-D harmonic waves. By using the simplest equation method, we find exact traveling wave solutions and a general form of the multiple-soliton solution of the DS model. The dispersion analysis as well as the conservation law of the DS system are discussed. It is revealed that the consistency of the results with the conservation of the potential energy increases with increasing Ursell parameter. Also, the stability of the ODEs form of the DS system is presented by using the phase portrait method.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Central China Normal University, 430079, Wuhan, China

    Ehab S. Selima & Xiaohua Yao

  2. Mathematics Department, Faculty of Science, Menoufia University, 32511, Shebin El-kom, Egypt

    Ehab S. Selima

  3. Mathematics Department, Faculty of science, Taibah University, Al-Ula, Saudi Arabia

    Aly R. Seadawy

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

    Aly R. Seadawy

Authors
  1. Ehab S. Selima
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  2. Aly R. Seadawy
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  3. Xiaohua Yao
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Correspondence to Aly R. Seadawy.

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Selima, E.S., Seadawy, A.R. & Yao, X. The nonlinear dispersive Davey-Stewartson system for surface waves propagation in shallow water and its stability. Eur. Phys. J. Plus 131, 425 (2016). https://doi.org/10.1140/epjp/i2016-16425-7

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  • DOI: https://doi.org/10.1140/epjp/i2016-16425-7

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