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 …

In this paper we review recent progress on the analysis, experimental exploration, and
application of elastic wave propagation in weakly nonlinear media and metamaterials. We …

In this paper, we study the characteristics of pure-quartic optical solitons in a nonlinear
medium having a weakly nonlocal response. We propose an nonlinear Schrödinger …

Stabilization of multidimensional solitons in self-focusing systems against the critical and
supercritical collapse is a fundamental problem of nonlinear-wave dynamics in diverse …

We study self-similar dynamics of picosecond light pulses generating in optical fiber
amplifiers and fiber lasers with distributed parameters. A rich variety of periodic and solitary …

This study presents higher-order multiple scales analysis aimed at revealing angle-and
amplitude-dependent invariant waveforms, and plane-wave stability, in two-dimensional …

We consider self-trapping of topological modes governed by the one-and two-dimensional
(1D and 2D) nonlinear-Schrödinger/Gross–Pitaevskii equation with effective single-and …

Dynamical and self-trapping properties of two-dimensional (2D) binary mixtures of Bose-
Einstein condensates in cross-combined lattices, consisting of a one-dimensional (1D) …

Abstract We analyze a Crank–Nicolson finite difference discretization for the perturbed (2+
1) D nonlinear Schrödinger equation with saturable nonlinearity and a perturbation of cubic …

Pulse propagating in inhomogeneous nonlinear media with linear/nonlinear gain and loss
described by the asymmetrical (2+ 1)-dimensional cubic-quintic Ginzburg-Landau equation …