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 …

We study existence, bifurcation and stability of two-dimensional optical solitons in the
framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with …

We address the existence and stability of localized modes in the framework of the fractional
nonlinear Schrödinger equation (FNSE) with the focusing cubic or focusing-defocusing …

We introduce a system combining the quadratic self-attractive or composite quadratic-cubic
nonlinearity, acting in the combination with the fractional diffraction, which is characterized …

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 …

We study soliton dynamics in a passive optical system governed by the Lugiato–Lefever
equation with effective diffraction represented by a fractional spatial derivative. Two models …

Currently, much interest is drawn to the analysis of optical and matter-wave modes
supported by the fractional diffraction in nonlinear media. We predict a new type of such …

Abstract Families of coupled solitons of PT PT-symmetric physical models with gain and loss
in fractional dimension and in settings with and without cross-interactions modulation (CIM) …

We investigate to the best of our knowledge the first time the interactions of in-phase and out-
of-phase Airy beams in Kerr, saturable and nonlocal nonlinear media with fourth-order …