求解耦合非线性Schrodinger-Boussinesq方程的三角标量辅助变量方法  

Trigonometric Scalar Auxiliary Variable Method for Coupled Nonlinear Schrodinger-Boussinesq Equation

作　　者：郭姣姣 庄清渠[1] GUO Jiaojiao;ZHUANG Qingqu(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2024年第1期98-107,共10页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金资助项目(11771083);福建省自然科学基金资助项目(2021J01306)。

摘　　要：采用三角标量辅助变量(TSAV)方法,构造求解耦合非线性Schrodinger-Boussinesq方程初边值问题的高效数值格式。基于方程非线性势能的三角函数形式,提出求解方程的TSAV格式;对方程在时间和空间上分别采用二阶Crank-Nicolson格式和傅里叶谱方法进行离散,并证明时间半离散格式的修正能量守恒律。最后,通过数值算例对文中格式进行验证。结果表明:文中格式具有有效性,修正能量具有守恒性。Based on the trigonometric scalar auxiliary variable(TSAV)method,an efficient numerical scheme is constructed to solve the initial boundary value problem of the coupled nonlinear Schrodinger-Boussinesq equation.Firstly,based on the trigonometric function form of the nonlinear potential energy equation,the TSAV scheme of the considered equation is proposed.Then,the equation is discretized in temporal and spatial by using the second-order Crank-Nicolson scheme and Fourier spectral method respectively,and the modified energy conservation law of time semi-discrete scheme is proved.Finally,the proposed scheme is verified by numerical examples.The results show that the proposed scheme is effective and the modified energy is conserved.

关 键 词：耦合非线性Schrodinger-Boussinesq方程 三角标量辅助变量方法 修正能量 守恒律 

分 类 号：O241.8[理学—计算数学]