对数非线性薛定谔方程基态解的数值解法

针对对数非线性薛定谔方程,本文构造了一种求基态解的数值解法.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方法来求正则化后的基态解.在求解的每个时间步我们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. 我们分析了正则化方法的能量误差,并通过数值模拟验证了本文方法的可靠性.

Numerical method for the ground state solution of Logarithmic nonlinear Schrodinger equation

In this paper, we construct a numerical method for computing the ground state solution of Logarithmic nonlinear Schr\"odinger equation. We first regularize the energy functional of the model, then compute the ground state solution by using the normalized gradient flow method. At each time step, we propose an implicit numerical scheme of the backward Euler Fourier spectral method, which is solved by fixed point iteration. In the end, we prove the estimation of energy error, and provide numerical simulation to verify the reliability of our method.