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We investigated three-dimensional quantum systems with higher-order dispersion and nonlinear effects. The systems’ soliton dynamics is studied based on the (3+1)-dimensional higher-order nonlinear Schrödinger equation (NLSE). Based on the self-similar approach and the bright soliton-type solution of the (1+1)-dimensional NLSE, we derived the analytical bright soliton solution for the (3+1)-dimensional NLSE with higher-order dispersion and nonlinear effects, with the typical soliton feature pictorially demonstrated. Our study illustrates that a higher-dimensional medium with higher-order dispersion and nonlinear effects supports soliton behavior. This demonstrates the applicability of the theoretical treatment presented in this work.