SOLITON INTERACTIONS FOR THE GENERALIZED (3+1)-DIMENSIONAL BOUSSINESQ EQUATION

Abstract

Generalized (3+1)-dimensional Boussinesq equation is investigated in this paper. Through the dependent variable transformation and symbolic computation, the one- and two-soliton solutions are obtained. With the one-soliton solution, the coefficient effects in the soliton propagation process are investigated. Through analyzing the two-soliton solution, two kinds of two-soliton interactions are presented: (i) Two solitons merge into a bigger one whose amplitude increases but does not exceed the sum of the two at the moment of the collision; (ii) Two solitons can pass through each other, and their shapes keep unchanged with a phase shift after the separation. In addition, two kinds of analytic solutions are discussed: (i) "Amplitudes" of the two analytic solutions immediately turn to negative (positive) infinity after the "collision"; (ii) Two analytic solutions are fused into a higher peak (valley) at the moment of "collision", whose "amplitudes" change to negative (positive) infinity after the separation.