广义Zakharov-Kuznetsov方程的多辛Preissmann格式

Multi-symplectic Preissmann methods for generalized Zakharov-Kuznetsov equation

广义Zakharov-Kuznetsov方程作为一类重要的非线性方程有着许多广泛的应用前景,基于Hamilton空间体系的多辛理论研究了广义Zakharov-Kuznetsov方程的数值解法,讨论了利用Preissmann方法构造离散多辛格式的途径,并构造了一种典型的半隐式的多辛格式,该格式满足多辛守恒律、局部能量守恒律.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性.

Generalized Zakharov-Kuznetsov equation, a typical nonlinear wave equation, was sdudied based on the multi-symplectic theory in Hamilton space. The multi-symplectic formulations of general- ized Zakharov-Ku-znetsov equation with several conservation laws are presented. The multi-symplectic preissmann method is used to discretize the formulations. The numerical experiment is given, and the resuits verify the effciency of the multi-symplectic scheme.