Riesz空间分数阶Klein-Gordon-Zakharov方程的保能量格式  

Energy-preserving scheme for Riesz space-fractional nonlinear Klein-Gordon-Zakharov equation

作　　者：刘莹 孙建强 孔嘉萌 LIU Ying;SUN Jianqiang;KONG Jiameng(College of Science,Hainan University,Haikou,Hainan 570228,China)

机构地区：[1]海南大学理学院,海南海口570228

出　　处：《山东科技大学学报（自然科学版）》2022年第6期104-109,共6页Journal of Shandong University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(11961020,11561018)。

摘　　要：首先利用傅里叶拟谱方法对Riesz空间分数阶导数离散近似,然后利用二阶平均向量场方法构造出Riesz空间分数阶非线性Klein-Gordon-Zakharov方程新的保能量格式,最后利用新的平均向量场格式数值模拟方程孤立波的演化行为。数值模拟结果表明,Riesz空间分数阶非线性Klein-Gordon-Zakharov方程的新格式可以精确地保持方程的能量守恒特性。Firstly, the Riesz space-fractional derivative is discretized by Fourier pseudo-spectral method. Then, a new energy-preserving scheme for Riesz space-fractional nonlinear Klein-Gordon-Zakharov equation is constructed by the second-order average vector field method. Lastly, the evolution behavior of solitary waves is simulated by applying the new average vector field scheme. Numerical simulated results show that the new scheme for Riesz space-fractional nonlinear Klein-Gordon-Zakharov equation can preserve the energy-preserving property accurately.

关 键 词：平均向量场方法 Klein-Gordon-Zakharov方程 傅里叶拟谱方法 Riesz空间分数阶导数 

分 类 号：O241.5[理学—计算数学]