Table 2 A comparison of present study and existing literature.

From: On certain novel numerical and analytical solutions for the pure-cubic Schrödinger equation in optical fibers with Kerr nonlinearity

Study

Model

Applied Techniques

Solutions achieved

Present study

The Pure-cubic NLSE with third-order dispersion, Kerr law nonlinearity, self-steepening, and higher-order nonlinear effects.

Polynomial Method, Extended Hyperbolic Function Method, Tanh Method, Adomian Decomposition Method

Bright solitons, dark solitons, singular solitons, and phase portraits

Akhmediev and Ankiewicz (1997)63

The Cubic NLSE and its applications to optical pulses

Inverse scattering, exact ansatz, bifurcation theory

Pulse propagation, modulation instability

Picozzi, A. (2014)64

The general NLSE with Kerr law in optical turbulence context

Statistical mechanics, wave condensation

Rogue waves, incoherent solitons, spectral cascades

Agrawal, G. P. (2019)65

The Generalized NLSE with Kerr effect for optical fiber systems

Analytical and numerical, split-step Fourier

Soliton pulses, higher-order soliton formation

Chen and Liu (2020)66

The Optical solitons governed by Schrödinger-type equations with Kerr law

Sine-cosine, Tanh-sech, G’/G expansion

Bright, dark, periodic solitons