Numerical simulation of fractal wave propagation of a multi-dimensional nonlinear fractional-in-space Schrödinger equation

Abstract

This paper studies a quantum particle traveling in a fractal space-time, which can be modelled by a fractional modification of the Schrödinger equation with variable coefficients. The Fourier spectral method is used to reveal the solution properties numerically, and the fractal properties are illustrated graphically by choosing different coefficients and different fractional orders. Some novel isosurface plots of the dynamics of pattern formation in the fractional Schrödinger equation with variable coefficients are shown.