N-fold Darboux transformation and solitonic interactions of a variable-coefficient generalized Boussinesq system in shallow water

Abstract

Under consideration in this paper is a variable-coefficient generalized Boussinesq system for the long weakly-nonlinear and weakly-dispersive surface waves in shallow water. With the aid of symbolic computation, N-fold Darboux transformation ( N-DT) is constructed for that system. Analytic solutions of the system are obtained via the N-DT. Elastic interactions of three bell-shaped and periodic bell-shaped solitons are obtained. Fusion interactions and periodic fusion–fission interactions of the solitary waves are graphically analyzed, which are inelastic.