Abstract
The soliton interactions, especially the soliton resonancephenomena of the (2+1)-dimensional Boussinesq equation have beeninvestigated numerically in this paper. Based on the Bridges'smulti-symplectic idea, the multi-symplectic formulations withseveral conservation laws for the (2+1)-dimensional Boussinesqequation are presented firstly. Then, a forty-five points implicitmulti-symplectic scheme is constructed. Finally, according to thesoliton resonance condition, numerical experiments on thetwo-soliton solution of the (2+1)-dimensional Boussinesq equationfor simulating the soliton interaction phenomena, especially thesoliton resonance are reported. From the results of the numericalexperiments, it can be concluded that the multi-symplectic schemecan simulate the soliton resonance phenomena perfectly, which canbe used to make further investigation on the interaction and theenergy distribution of gravity waves, and evaluate the impact onthe ship traffic on the surface of water.
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