摘要
本文针对对数非线性薛定谔方程构造了一种求其基态解的数值解法.该方法首先对原始能量泛函进行正则化处理,然后使用归一化梯度流来求正则化后的基态解,其中,在求解的每个时间步采用向后欧拉傅里叶谱方法的隐式数值格式,并通过不动点迭代求解.本文分析了该方法的能量误差,并通过数值模拟验证其可靠性.
We construct a numerical method for computing the ground state solution of logarithmic nonlinear Schrodinger equation. We firstly regularize the energy functional of the model and then compute the ground state solution by using the normalized gradient flow method. At each time step, an implicit numerical scheme of the backward Euler Fourier spectral method is proposed and solved by fixed point iteration. In the end, we analyze the energy error of the method and provide numerical simulation to verify it’s reliability.
作者
冯子旭
何维清
张世全
FENG Zi-Xu;HE Wei-Qing;ZHANG Shi-Quan(School of Mathematics,Sichuan University,Chengdu 610064)
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2021年第5期15-20,共6页
Journal of Sichuan University(Natural Science Edition)
基金
国家自然科学基金(11971335)。
关键词
基态解
对数薛定谔方程
正则化
归一化梯度流
后向欧拉傅里叶谱方法
Ground state solution
Logarithmic Schrodinger equation
Regularization
Normalized gradient flow
Backward Euler Fourier spectral method
