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Explicit solutions of the Schamel–KdV equation employing Darboux transformation

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Abstract

The aim of this paper is to derive a class of soliton solutions of the Schamel–KdV (SKdV) equation employing Darboux transformation with the help of the Lax pair. The SKdV equation is reduced to a suitable form by means of an effective transformation so that the Lax pair of the said equation can be derived using the Ablowitz–Kaup–Newell–Segur (AKNS) method. For the first time, we apply Darboux transformation through the Lax pair so as to obtain an effective solution to the SKdV equation, and this allows us to investigate new classes of soliton solutions of the SKdV equation. These solutions provide some new wave features, W-shaped soliton, breather-type soliton, etc. Effects of the nonlinear and dispersion coefficients are demonstrated numerically through two-dimensional graphs. Finally, for a better understanding of the dynamics of the model, some key three-dimensional plots of the wave solutions are presented.

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Acknowledgements

The authors are thankful to the reviewers for their valuable comments and suggestions which helped to improve the quality of the paper. There is no funding for this research work.

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Authors and Affiliations

  1. Department of Mathematics, Siksha Bhavana, Visva-Bharati, Santiniketan, 731 235, India

    Prasanta Chatterjee & Dipan Saha

  2. Department of Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

    Abdul-Majid Wazwaz

  3. Department of Mathematics, Mathabhanga College, Cooch Behar, 736 164, India

    Santanu Raut

Authors
  1. Prasanta Chatterjee
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  2. Dipan Saha
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  3. Abdul-Majid Wazwaz
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  4. Santanu Raut
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Correspondence to Santanu Raut.

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Chatterjee, P., Saha, D., Wazwaz, AM. et al. Explicit solutions of the Schamel–KdV equation employing Darboux transformation. Pramana - J Phys 97, 172 (2023). https://doi.org/10.1007/s12043-023-02657-3

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  • DOI: https://doi.org/10.1007/s12043-023-02657-3

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