非线性耦合Schrdinger-KdV方程组的一个局部能量守恒格式

A LOCAL ENERGY CONSERVATIVE SCHEME FOR NONLINEAR COUPLED SCHRDINGER-KDV EQUATIONS

本文利用平均值离散梯度给出了一个构造哈密尔顿偏微分方程的局部能量守恒格式的系统方法．并用非线性耦合Schrodinger-KdV方程组加以说明．证明了格式满足离散的局部能量守恒律，在周期边界条件下，格式也保持离散整体能量及系统的其它两个不变量．最后数值实验验证了理论结果的正确性．

In this paper, by using the mean value discrete gradient, we give a systematic method to construct a local energy conservative scheme for Hamiltonian PDEs. This method is illustrated by nonlinear coupled SchrSdinger-KdV equations. We prove that the scheme satisfies the discrete local energy conservation law, with the periodic boundary conditions, the scheme also conserves the discrete global energy and other two invariants. Finally, Numerical experiments are presented to verify the accuracy of theoretical results.