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Multi-shock and soliton solutions of the Burgers equation employing Darboux transformation with the help of the Lax pair

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Abstract

The purpose of this article is to derive a class of multi-soliton solutions of the Burgers equation employing Darboux transformation with the help of the Lax pair. By means of an effective transformation, the Burgers equation is reduced to a suitable form, and accordingly, the Lax pair of the said equation is derived utilising the Ablowitz–Kaup–Newell–Segur (AKNS) approach. Thus, the integrability of the Burgers equation is confirmed. To find an effective solution for the Burgers equation, for the first time, we apply the Darboux transformation through the Lax pair and explore new types of one-soliton solutions and two-soliton solutions of the Burgers equation. These solutions provide some new features of the Burgers equation. To the best of our knowledge, this is the first study in which a parabolic type of structure is found in the Burgers system. Moreover, taking these solutions as the seed solution, higher-order multi-soliton solution can also be generated. Finally, some important three-dimensional plots of the wave solutions are presented to visualise the dynamics of the model.

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Authors and Affiliations

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

    Dipan Saha & Prasanta Chatterjee

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

    Santanu Raut

Authors
  1. Dipan Saha
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  2. Prasanta Chatterjee
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  3. Santanu Raut
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Correspondence to Santanu Raut.

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Saha, D., Chatterjee, P. & Raut, S. Multi-shock and soliton solutions of the Burgers equation employing Darboux transformation with the help of the Lax pair. Pramana - J Phys 97, 54 (2023). https://doi.org/10.1007/s12043-023-02534-z

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  • DOI: https://doi.org/10.1007/s12043-023-02534-z

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