分数阶Klein-Gordon-Schrödinger方程的保能量方法

该文先将分数阶Klein-Gordon-Schrödinger方程转化成辛结构的哈密尔顿系统,利用傅里叶拟谱方法对Riesz空间分数阶导数进行近似离散,得到分数阶Klein-Gordon-Schrödinger方程有限维哈密尔顿系统; 再利用2阶平均向量场方法对有限维哈密尔顿系统离散,得到分数阶Klein-Gordon-Schrödinger方程新的保能量格式; 最后利用新的保能量格式数值模拟方程孤立波的演化行为,并分析新格式的保能量守恒特性.

The Energy-Preserving Method for the Fractional Klein-Gordon-Schrödinger Equation

The fractional Klein-Gordon-Schrödinger equation are transformed into the Hamiltonian system with the symplectic structure.The Riesz space-fractional derivation is discretized approximately by the Fourier pseudo-pectral method.The finite dimensional Hamiltonian system of the fractional Klein-Gordon-Schrödinger equation is obtained.The second order average vector field method is applied to solve the finite dimensional Hamiltonian system.The new energy preserving scheme of the fractional Klein-Gordon-Schrödinger equation is obtained.The new scheme is applied to numerically simulate the solitary evolution behaviors of the equation,moreover the energy conservation property of the new scheme is investigated.