具有波动算子的非线性Schrdinger方程的多辛格式及其守恒律

Muti-symplectic Scheme and Conservation Laws of Nonlinear Schrdinger Equation with Wave Operator

本文所讨论的具有波动算子的非线性Schro¨dinger方程的具有多辛结构,从而把它写成Hamilton正则方程组的形式,导出其多辛守恒律及多辛格式.用隐式中点公式离散多辛方程组得到多辛Preissman积分.它的多辛格式具有离散多辛守恒律。我们用数值实验验证了理论分析的正确性.

Nonlinear Schroedinger equation with wave operator has multi- symplectic structure, we turn it into mulit- symplectic Hamihonian formulations. We find its multi - symplectic conservation laws and multi - symplectic scheme. We get the Preissman multi - symptectic integrator via implicit midpoint rule. Its multi - symplectie scheme possess discrete multi - symplectic law. Numerical experiments suggest the correction of the theoretic analysis.