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

Ying-ying Sun and Wan-yi Sun

Applied Mathematics and Computation, 2022, vol. 421, issue C

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.

Keywords: Boussinesq equation; Bäcklund transformation; Darboux transformation; Halphen equation; Elliptic N-soliton solutions (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000509

DOI: 10.1016/j.amc.2022.126964

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