Analytical and approximate solutions of nonlinear Schrodinger equation with higher dimension in the anomalous dispersion regime

The generalized Riccati equation mapping method (GREMM) is used in this paper to obtain different types of soliton solutions for nonlinear Schrodinger equation with higher dimension that existed in the regimes of anomalous dispersion. Later, we use the q-homotopy analysis method combined with the Laplace transform (q-HATM) to obtain approximate solutions of the bright and dark optical solitons. The q-HATM illustrates the solutions as a rapid convergent series. In addition, to show the physical behavior of the solutions obtained by the proposed techniques, the graphical representation has been provided with some parameter values. The findings demonstrate that the proposed techniques are useful, efficient and reliable mathematical method for the extraction of soliton solutions.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Automated summary

The generalized Riccati equation mapping method (GREMM) is used to obtain various soliton solutions for the nonlinear Schrödinger equation with higher dimension in the regime of anomalous dispersion. The q-homotopy analysis method combined with the Laplace transform (q-HATM) is employed to obtain approximate solutions for bright and dark optical solitons, which are represented as rapidly convergent series. The proposed techniques are demonstrated to be useful, efficient, and reliable mathematical methods for extracting soliton solutions.