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Conservative Difference Scheme of Solitary Wave Solutions of the Generalized Regularized Long-Wave Equation

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Abstract

Conservative difference scheme for the nonlinear dispersive generalized regularized long-wave (GRLW) equation is proposed. Existence of its difference solutions has been shown. It is proved by the discrete energy method that the difference scheme is uniquely solvable, unconditionally stable and the convergence is of second-order in the maximum norm. The particular case known as the modified regularized long-wave (MRLW) equation is also discussed numerically in details. Furthemore, three invariants of motion are evaluated to determine the conservation properties of the problem. Interaction of two and three solitary waves are shown. Some numerical examples are given in order to validate the theoretical results.

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Acknowledgement

The authors are grateful to the reviewers valuable comments and suggestions that improved the manuscript.

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Authors and Affiliations

  1. Institut Supérieur des Sciences Appliquées et de Technologie de Sousse, Université de Sousse, 4003 Sousse Ibn Khaldoun, Sousse, Tunisia

    Asma Rouatbi, Manel Labidi & Khaled Omrani

Authors
  1. Asma Rouatbi
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  2. Manel Labidi
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  3. Khaled Omrani
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Correspondence to Asma Rouatbi, Manel Labidi or Khaled Omrani.

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Rouatbi, A., Labidi, M. & Omrani, K. Conservative Difference Scheme of Solitary Wave Solutions of the Generalized Regularized Long-Wave Equation. Indian J Pure Appl Math 51, 1317–1342 (2020). https://doi.org/10.1007/s13226-020-0468-7

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  • DOI: https://doi.org/10.1007/s13226-020-0468-7

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