论文标题
对数schrodinger方程的数值研究，具有排斥谐波电位
Numerical study of the logarithmic Schrodinger equation with repulsive harmonic potential
论文作者
论文摘要
我们考虑具有对数非线性和排斥谐波潜力的Schrodinger方程。根据方程的参数，解决方案可能是分散的，也可能不是分散的。当发生分散时，它的时间呈指数率。为了控制这一点，我们通过广义透镜变换更改未知功能。这种方法中和可能的边界效应，可以在没有潜力的情况下使用Schrodinger方程。然后，在对数非线性被正规化之后，我们通过非均匀网格在新方程式上采用标准分裂方法。我们还讨论了功率非线性的情况，并给出了有关两种非线性案例的一阶Lie-Trotter分裂方法的误差估计的一些结果。最后，据报道，广泛的数值实验研究了方程的动力学。
We consider the Schrodinger equation with a logarithmic nonlinearity and a repulsive harmonic potential. Depending on the parameters of the equation, the solution may or may not be dispersive. When dispersion occurs, it does with an exponential rate in time. To control this, we change the unknown function through a generalized lens transform. This approach neutralizes the possible boundary effects, and could be used in the case of the Schrodinger equation without potential. We then employ standard splitting methods on the new equation via a nonuniform grid, after the logarithmic nonlinearity has been regularized. We also discuss the case of a power nonlinearity and give some results concerning the error estimates of the first-order Lie-Trotter splitting method for both cases of nonlinearities. Finally extensive numerical experiments are reported to investigate the dynamics of the equations.
