A survey of recent theoretical and experimental studies on localized structures that form and
propagate in a broad class of optical and matter-wave media is presented. The article is …

The article produces a brief review of some recent results which predict stable propagation
of solitons and solitary vortices in models based on the nonlinear Schrödinger equation …

This review article provides a concise summary of one-and two-dimensional models for the
propagation of linear and nonlinear waves in fractional media. The basic models, which …

Interest in physical systems with fractional derivatives has exploded in the 21st century.
Similarly, interest in the localized excitations of nonlinear dynamical systems continues to …

We construct a family of bright optical solitons composed of fundamental-frequency (FF) and
second-harmonic (SH) components in the one-dimensional (planar) waveguide with the …

The plan of this study is to construct analytical exact solutions of space-time fractional
Calogero-Degasperis equation and space-time fractional Sharma-Tasso-Olver equation …

We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the
propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms …

We consider phase transitions, in the form of spontaneous symmetry breaking (SSB)
bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self …

The M-shaped solitons—a special type of solitons—have been reported in many models,
while most of them are not focused on the commonly used nonlinear Schrödinger equation …

We demonstrate W-shaped solitons sustained under the inhomogeneous self-defocusing
Kerr nonlinearity in the nonlinear Schrӧdinger equation. These solitons are dark or gray …