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.

翻译：我们用对数非线性和令人厌恶的调和潜力来考虑施罗德宁格方程式。 取决于方程式的参数, 解决办法可能是分散的, 也可能不是分散的。 当分散发生时, 它会使用指数速度。 为了控制它, 我们通过一个通用的透镜变换来改变未知的函数。 这种方法可以排除可能的边界效应, 并且可以在施罗德因格方程式中毫无潜力地使用。 然后在对数非线性已经正规化之后, 我们再通过非统一格式格式对新方程式采用标准分解方法。 我们还讨论权力非线性的情况, 并给出一些结果, 说明对两种非线性情况下的利- 特拉特第一级分解法的错误估计。 最后报告了广泛的数字实验, 以调查方程式的动态 。