非线性Pochhammer-Chree方程的多辛盒格式及孤立波试验

Multi-symplectic box scheme for nonlinear Pochhammer-Chree equation and solitary wave experiments

对非线性Pochhammer-Chree方程的一个多辛方程组进行数值离散,导出了方程的离散多辛守恒律,并得到一个与此数值离散方法等价的新的9点多辛盒格式.孤立波的数值模拟试验验证了所构造格式的长时间数值稳定性以及非线性Pochhammer-Chree方程的孤立波相互作用是非弹性的事实.

By discretizing the multi - symplectic systems, the discretized multi - symplectic conservation laws for the nonlinear Pochhammer -Chree equation is derived. Then a new nine -point multi - symplectic box scheme which is equivalent to the discretized method is obtained. Numerical experiments show that the scheme constructed in this paper has excellent long - time numerical behavier. Numerical studies also indicate that the interaction of these solitary waves is inelastic.