Bright soliton dynamics in higher-dimensional system with power-law nonlinearity

For power-law nonlinear system in higher-dimensional setting like the three-dimensional case, we derived its bright soliton solution with specific power-law feature based on the self-similar method. The dynamical evolution pattern of the derived solution is pictorially demonstrated which illustrates the typical bright soliton feature. The theoretical results presented in this work can be used to guide experimental observation of soliton behavior in higher-dimensional system with power-law nonlinearity.