In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochastic nonlinear Schrodinger equations.It is shown that the stochasticmulti-symplecticmethod preserves themultisymplectic structure,the discrete charge conservation law,and deduces the recurrence relation of the discrete energy.Numerical experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.
Based on splitting multi-symplectic structures, a new multi-symplectic scheme is proposed and applied to a nonlinear wave equation. The explicit multi-symplectic scheme of the nonlinear wave equation is obtained, and the corresponding multi-symplectic conservation property is proved. The backward error analysis shows that the explicit multi-symplectic scheme has good accuracy. The sine-Gordon equation and the KleinGordon equation are simulated by an explicit multi-symplectic scheme. The numerical results show that the new explicit multi-symplectic scheme can well simulate the solitary wave behaviors of the nonlinear wave equation and approximately preserve the relative energy error of the equation.
A newscheme for the Zakharov-Kuznetsov(ZK)equationwith the accuracy order of O(△t^(2)+△x+△y^(2))is proposed.The multi-symplectic conservation property of the new scheme is proved.The backward error analysis of the newmulti-symplectic scheme is also implemented.The solitary wave evolution behaviors of the Zakharov-Kunetsov equation is investigated by the new multi-symplectic scheme.The accuracy of the scheme is analyzed.
