Interactions of solitons in a variable-coefficient generalized Boussinesq system in shallow water

Under consideration in this paper is a variable-coefficient generalized Boussinesq (gBq) system, which can model the propagation of long weakly nonlinear and weakly dispersive surface waves in shallow water. With the aid of the Darboux transformation and symbolic computation, soliton solutions of the gBq system are obtained that do not have singularities under a selection of the spectral parameters. Interactions of the solitons with the elastic properties are discussed. The outcome of this paper might be of some help for the investigation of nonlinear and dispersive problems in fluid dynamics.