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

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 …

From protein motifs to black holes, topological solitons are pervasive nonlinear excitations
that are robust and can be driven by external fields. So far, existing driving mechanisms all …

A comprehensive review of spatiotemporal pattern formation in systems driven away from
equilibrium is presented, with emphasis on comparisons between theory and quantitative …

The structure and dynamics of one-dimensional binary Bose gases forming quantum
droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two …

The current research into solitons and their use in fiber optic communications is very
important to the future of communications. Since the advent of computer networking and …

A salient feature of solid-state quantum-Hall-type topological materials in two dimensions is
the presence of conducting electronic edge states that are insensitive to scattering by …

Soliton molecules can be formed in some possible mechanisms both theoretically and
experimentally. In this paper, we introduce a new mechanism, namely the velocity resonant …

This review is dedicated to recent progress in the active field of rogue waves, with an
emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector …