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

Abstract:

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 based on the backward Euler Fourier spectral method is used and solved by fixed point iteration. Finally we analyze the energy error and provide a numerical simulation to verify th e reliability of the method.