多辛sine-Gordon方程高阶保能量格式

The High Order Energy-Preserving Scheme of Multi-Symplectic sine-Gordon Equation

1维sine-Gordon方程通过适当的变换转化成相应多辛Hamilton偏微分方程,其中与时间变量偏导数有关的矩阵是可逆的,利用Hamilton系统的4阶平均向量场方法和Boole离散线积分方法得到了多辛sine-Gordon方程的一个新的4阶整体保能量格式.利用新格式数值模拟sine-Gordon方程.数值结果表明:新格式能较好地模拟sine-Gordon方程在不同初值条件下孤立波的运动,且保持了孤立波的能量守恒特性.

One dimension sine-Gordon equation is transformed into the multi-symplectic Hamiltonian partial differential equation through appropriate transformation,where the matrix with the time variable partial derivation is inverse.A new fourth-order energy-preserving scheme of multi-symplectic sine-Gordon equation is obtained by the fourth order average vector field method of the Hamiltonian system and the Boole discrete line integral method.The new scheme is applied to simulate sine-Gordon equation.Numerical results show that the new scheme can well simulate the solitary wave behaviors of sine-Gordon equation with different initial conditions,moreover preserve the energy conservation property of the solitary waves.