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中文摘要：
广义Boussinesq方程作为一类重要的非线性方程有着许多有趣的性质，基于Hamilton空间体系的多辛理论研究了广义Boussinesq方程的数值解法，构造了一种等价于多辛Box格式的新隐式多辛格式，该格式满足多辛守恒律、局部能量守恒律和局部动量守恒律．对广义Boussinesq方程孤子解的数值模拟结果表明，该多辛离散格式具有较好的长时间数值稳定性．
英文摘要：
Generalized Boussinesq equation, representing a group of important nonlinear equations, possesses many interesting properties. The multi-symplectic formulations of which in Hamilton space were introduced. Then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme was constructed to solve the partial differential equations （PDEs） that were derived from the generalized Boussinesq equation. The numerical experiments on the soliton solutions of the generalized Boussinesq equation were also reported. Finally, the results of which show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equation.
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