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

There are two main aims of this paper. One is to present a Backlund transformation which connects the continuous to discrete Boussinesq system. We note that it is an update of Backlund transformation given in [1] . The other one is to apply this Backlund 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.(c) 2022 Elsevier Inc. All rights reserved.