Properties of some higher-dimensional nonlinear Schrödinger equations

•The (2 + 1) and (3 + 1) dimensional nonlinear Schrödinger equations are studied.•The sub equation method is used.•The obtained numerical results are presented by Figures.•Our findings can help us to understand the physical significance of many nonlinear models derived from nonlinear sciences. In this study, we have used the sub-equation method to provide some analytic solutions of the (2 + 1) and (3 + 1) dimensional nonlinear Schrödinger equations (NLSEs). We obtained are dark, bright and singular optical solitons. We observed through the Mathematica 11.2 program that these solutions provide the equations. Apart from that, we have shown the graphics performance of some of the solutions found. This method has been used recently to obtain exact traveling wave solutions of nonlinear partial differential equations.