Dark soliton dynamics for quantum systems with higher-order dispersion and higher-order nonlinearity

In this work, we investigated one-dimensional and two-dimensional quantum systems with higher-order dispersions and higher-order nonlinear interactions. Based on the high-order nonlinear Schrödinger equation (NLSE) and via the F-expansion method, we derived the analytical dark soliton solution for the one-dimensional system first. By applying the self-similar method and using the results of the one-dimensional case, the analytical dark soliton solution of the system in the two-dimensional case was derived. The dynamic evolution pattern of the two-dimensional dark soliton is pictorially demonstrated. The theoretical results of our work can be used to guide the detection and experimental study of dark soliton in a two-dimensional quantum system, using high-order dispersion and higher-order nonlinear interactions.