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An update of a Bäcklund transformation and its applications to the Boussinesq system

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  • Sun, Ying-ying
  • Sun, Wan-yi

Abstract

There are two main aims of this paper. One is to present a Bäcklund transformation which connects the continuous to discrete Boussinesq system. We note that it is an update of Bäcklund transformation given in [1]. The other one is to apply this Bäcklund transformation to establish the Lax pair and N-times Darboux transformation for the continuous Boussinesq equation. Starting from an elliptic seed solution, the Darboux transformation is used to construct explicit solutions. Dynamics of the solutions obtained from 1-time Darboux transformation are analyzed and illustrated.

Suggested Citation

  • Sun, Ying-ying & Sun, Wan-yi, 2022. "An update of a Bäcklund transformation and its applications to the Boussinesq system," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000509
    DOI: 10.1016/j.amc.2022.126964
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    References listed on IDEAS

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    1. Ma, Wen-Xiu, 2021. "Binary Darboux transformation for general matrix mKdV equations and reduced counterparts," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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