Elastic and inelastic interactions of solitons for a variable-coefficient generalized dispersive water-wave system

Under consideration in this paper is a variable-coefficient generalized dispersive water-wave system which can model the propagation of the long weakly nonlinear and weakly dispersive surface waves of variable depth in shallow water. With the aid of symbolic computation and N-fold Darboux transformation, multi-soliton solutions of the system are obtained. It is found that solitonic interactions could be either the inelastic fusion-fission or elastic ones, depending on different choices of the variable coefficients. With the parameters periodically varying with time, waves change their shapes while the fusion-fission interactions also coexist and are periodic.