A novel approach to explore optical solitary wave solution of the improved perturbed nonlinear Schrödinger equation

The present study aims to analyze the improved perturbed nonlinear Schrödinger equation with a Kerr law nonlinearity that governs the soliton propagation dynamics in optical fibre through nano-optical fibre. Improved perturbed nonlinear Schrödinger equation is investigated using the Hirota bilinear method and generalized extended auxiliary equation mapping architectonic. The influence of quantic non-linearity on the propagation of ultra-short optical pulses in a non-kerr medium, analogous to optical fibre, is depicted by the improved perturbed nonlinear Schrödinger equation. The goal here is to explore different optical soliton solutions such as singular, periodic, doubly periodic, bright dromion (soliton), trigonometric, dark singular, plane wave solution, combined optical solitons, rational and hyperbolic solutions etc using generalized extended auxiliary equation mapping architectonic method while parabolic, M-shaped, S-shaped, bright and anti-dark soliton solutions are obtained using Hirota bilinear method. Several entirely new optical solitary wave solutions have been discovered. These results are very useful in the study of optical logic switches and ultrashort pulse lasers. By assigning appropriate values to the parameters, a graphical representation (3D, 2D and contour plots) of the optical solitary wave solutions are also provided, which aids in the conceptual understanding of the model’s physical phenomena. The techniques used in this analysis are effective and powerful, as evidenced by the computational work and results. Higher-order NLSEs can also be solved using these techniques.