Novel constructed dark, bright and rogue waves of three models of the well-known nonlinear Schrödinger equation

Abstract

In this work, three models of the nonlinear Schrödinger equation are looked at to see if traveling wave solutions have unique structures. “The generalized Korteweg–de Vries, (2+1)-dimensional Ablowitz–Kaup–Newell–Segur, and the Maccari models” are among the examined systems. The kinetic energy operator is affected by where the mass is, how it changes over time, and how the kinetic energy operator is shown. Using the generalized Riccati expansion method, new soliton wave solutions are constructed for the models that have been looked at. Several different graphics depict the numerical simulations of the deduced answers. Verifying and improving these methods (Mathematica 13.1) means checking to see if they are right and re-entering the results into the models.