In this topical review paper we provide a survey of classical and more recent results on the
IST for one-dimensional scalar, vector and square matrix NLS systems on the line (-∞< …

Solitons are a class of nonlinear stable, localized waves. They arise widely in physical
problems; applications include water waves, plasma physics, Bose–Einstein condensation …

In this paper, we propose an integrable fractional derivative nonlinear Schrödinger (fDNLS)
equation with the aid of the completeness of the squared eigenfunctions for the Kaup …

According to the integrable nonlinear model introduced by Ablowitz et al. with the Riesz
fractional derivative, we discuss the inverse scattering transform, anomalous dispersion …

The Darboux transformation (DT) and generalized DT (GDT) have played important roles in
constructing multisoliton solutions, rogue wave solutions, and semirational solutions of …

In this paper, we propose a new integrable fractional Fokas–Lenells equation by using the
completeness of the squared eigenfunctions, dispersion relation, and inverse scattering …

Fiber optic research continues to develop due to the need for fast information technology.
The input signal in an optical fiber is in the form of a soliton wave that propagates in the fiber …

Fractional calculus highlights its importance and has been expanded to many fields. This
paper focuses on fractional integrable systems and their novel structural solutions to comply …

This article combines the Riemann–Hilbert method with fractional power-law time-varying
spectrum for the first time to solve a time fractional nonisospectral complex mKdV …

The perturbed Gerdjikov–Ivanov equation has immersed applications and significance in
photonic crystal fibers and fiber optics. Extracting soliton solutions of the proposed equation …