摘要
该文将2维G-P方程转化成无限维哈密尔顿系统,利用傅里叶拟谱方法和平均向量场方法对方程分别进行空间和时间离散得到方程的数值离散格式,基于快速傅里叶变换分解谱矩阵得到了2维G-P方程的快速保能量计算格式,利用新的保能量格式数值模拟方程孤立波演化行为,并分析了新格式的保能量守恒特性.
In this paper,the two-dimensional Gross-Pitaevskii(G-P)equation is transformed into an infinite-dimensional Hamiltonian system.By discretizing the equation spatially via the Fourier pseudo-spectral method and temporally using the average vector field(AVF)method,the numerical discretization schemes are derived.The rapid computational schemes for the two-dimensional G-P equation are further developed by decomposing the spectral matrix via the fast Fourier transform(FFT).Consequently,the novel energy-preserving schemes are established.The proposed schemes are employed to numerically simulate evolution of solitary waves in the equation and its energy conservation properties are analyzed.
作者
陈杰
孙建强
CHEN Jie;SUN Jianqiang(School of Mathematics and Statistics,Hainan University,Haikou Hainan 570228,China;Key Laboratory of Engineering Modeling and Statistical Computationof Hainan Province,Hainan University,Haikou Hainan 570228,China)
出处
《江西师范大学学报(自然科学版)》
北大核心
2025年第5期519-525,共7页
Journal of Jiangxi Normal University(Natural Science Edition)
基金
海南省自然科学基金(124MS001)
海南省工程建模与统计计算重点实验室开放课题(HNGCTJ2402)
国家自然科学基金(11961020)资助项目。
关键词
平均向量场方法
2维G-P方程
傅里叶拟谱方法
快速傅里叶变换
average vector field method
two-dimensional G-P equation
Fourier pseudo-spectral method
fast Fourier transform
