New physical structures and patterns to the optical solutions of the nonlinear Schrödinger equation with a higher dimension

Abstract

Abstract It is commonly recognized that, despite current analytical approaches, many physical aspects of nonlinear models remain unknown. It is critical to build more efficient integration methods to design and construct numerous other unknown solutions and physical attributes for the nonlinear models, as well as for the benefit of the largest audience feasible. To achieve this goal, we propose a new extended unified auxiliary equation technique, a brand-new analytical method for solving nonlinear partial differential equations. The proposed method is applied to the nonlinear Schrödinger equation with a higher dimension in the anomalous dispersion. Many interesting solutions have been obtained. Moreover, to shed more light on the features of the obtained solutions, the figures for some obtained solutions are graphed. The propagation characteristics of the generated solutions are shown. The results show that the proper physical quantities and nonlinear wave qualities are connected to the parameter values. It is worth noting that the new method is very effective and efficient, and it may be applied in the realisation of novel solutions.