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 …

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 …

The interaction of fractional diffraction and parity-time (PT) symmetric would bring some
unique properties to certain physical system. Here we report a spontaneous symmetry …

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 elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equation based on an
appropriately modified definition of the Riesz fractional derivative, which is characterized by …

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 present work investigates symmetry breaking in dual-core couplers with fractional
dispersion, cubic self-focusing, gain and loss effects acting in each core, modeled by …

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 …

In this paper, we investigate the new two-Lévy-index fractional nonlinear Schrödinger
(FNLS) equations with optical lattices, where two fractional derivative terms are introduced to …