Multi-symplectic method to simulate Soliton resonance of (2+1)-dimensional      Boussinesq equation

Weipeng Hu; Zichen Deng; Yuyue Qin

doi:10.3934/jgm.2013.5.295

Article Contents

2013, Volume 5, Issue 3: 295-318. Doi: 10.3934/jgm.2013.5.295

This issue Previous Article Smooth perfectness for the group of diffeomorphisms Next Article On Euler's equation and 'EPDiff'

Multi-symplectic method to simulate Soliton resonance of (2+1)-dimensional Boussinesq equation

1.
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an, Shaanxi, 710072

Received: December 31, 2012

Revised: June 30, 2013

Published: August 2013

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Abstract

The soliton interactions, especially the soliton resonance phenomena of the (2+1)-dimensional Boussinesq equation have been investigated numerically in this paper. Based on the Bridges's multi-symplectic idea, the multi-symplectic formulations with several conservation laws for the (2+1)-dimensional Boussinesq equation are presented firstly. Then, a forty-five points implicit multi-symplectic scheme is constructed. Finally, according to the soliton resonance condition, numerical experiments on the two-soliton solution of the (2+1)-dimensional Boussinesq equation for simulating the soliton interaction phenomena, especially the soliton resonance are reported. From the results of the numerical experiments, it can be concluded that the multi-symplectic scheme can simulate the soliton resonance phenomena perfectly, which can be used to make further investigation on the interaction and the energy distribution of gravity waves, and evaluate the impact on the ship traffic on the surface of water.

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Mathematics Subject Classification: Primary: 35G20, 65M06; Secondary: 35Q35.

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