Abstract Complex Ginzburg–Landau (CGL) equations serve as canonical models in a great
variety of physical settings, such as nonlinear photonics, dynamical phase transitions …

We give a general overview of the high-frequency regime in periodically driven systems and
identify three distinct classes of driving protocols in which the infinite-frequency Floquet …

The fractional Schrödinger equation (FSE)—a natural extension of the standard Schrödinger
equation—is the basis of fractional quantum mechanics. It can be obtained by replacing the …

Since the realization of Bose–Einstein condensates (BECs) trapped in optical potentials,
intensive experimental and theoretical investigations have been carried out for bright and …

This article offers a comprehensive survey of results obtained for solitons and complex
nonlinear wave patterns supported by nonlinear lattices (NLs), which represent a spatially …

One of generalized higher-order Schrödinger equation is considered. Equation has been
studied a few times using some special methods. We analyze the equation taking into …

We review both theoretical and experimental advances in the recently emerged field of
modulated photonic lattices. These artificial periodic dielectric structures provide a powerful …

Nonlinear systems with periodic variations of nonlinearity and/or dispersion occur in a
variety of physical problems and engineering applications. The mathematical concept of …

The phenomenon of Bose–Einstein condensation is a phase transition originally predicted
by Bose and Einstein in 1924. In particular, it was shown that below a critical temperature T …

To study controlled evolution of nonautonomous matter–wave solitons in spinor Bose–
Einstein condensates with spatiotemporal modulation, we focus on a system of three …