Related papers: Nonlinear wave dynamics near phase transition in $…
In the present paper we consider an optical system with a $\chi^{(2)}$-type nonlinearity and unspecified $\mathcal{PT}$-symmetric potential functions. Considering this as an inverse problem and positing a family of exact solutions in terms…
We investigate the switching dynamics in a $\mathcal{PT}$-symmetric fiber coupler composed of a saturable nonlinear material as the core. In such a saturable nonlinear medium, bistable solitons may evolve due to the balance between…
We determine the nonlinear stability of shock-fronted travelling waves arising in a reaction-nonlinear diffusion PDE, subject to a fourth-order spatial derivative term multiplied by a small parameter $\varepsilon$ that models {\it nonlocal…
Steady-state and transient antiplane dynamic processes in a structured solids consisting of uniform periodic square-cell lattices connected by a lattice layer of different bond stiffnesses and point masses are analyzed. A semi-infinite…
We investigate linear interference of a plane wave with different localised waves using coupled Fokas-Lenells equation(FLE) with four wave mixing (FWM) term. We obtain localised wave solution of the coupled FLE by linear superposition of…
We consider reflectionless wave propagation in networks modeled in terms of the nonlocal nonlinear Schr\"odinger (NNLS) equation on metric graphs, for which transparent boundary conditions are imposed at the vertices. By employing the…
We consider the nonlinear Helmholtz (NLH) equation describing the beam propagation in a planar waveguide with Kerr-like nonlinearity under non-paraxial approximation. By applying the Lie symmetry analysis, we determine the Lie point…
A model of nonlinear elastic medium with internal structure is considered. The medium is assumed to contain cavities, microcracks or blotches of substances that differ sharply in physical properties from the base material. To describe the…
The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by…
Paraxial linear propagation of light in an optical waveguide with material gain and loss is governed by a Schr\"odinger equation with a complex potential. Properties of parity-time-symmetric complex potentials have been heavily studied…
Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled mode equations (NLCME). This system of PDEs, similar in…
A statistical mechanic study of the $XY$ model with nonlinear interaction is presented on bipartite sparse random graphs. The model properties are compared to those of the $p$-clock model, in which the planar continuous spins are…
Nonlinear optical phenomena are typically local. Here we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms…
We present the research of ocean surface wind waves excitation in non-homogeneous situations, on the example of deep water strait in presence of the constant wind, blowing perpendicular to the coastal line. The used statistical wave model…
Parity-time (PT) symmetry gives rise to unusual phenomena in many physical systems, presently attracting a lot of attention. One essential and non-trivial task is the fabrication and design of the PT-symmetric lattices in different systems.…
We address the existence and stability of spatial localized modes supported by a parity-time-symmetric complex potential in the presence of power-law nonlinearity. The analytical expressions of the localized modes, which are Gaussian in…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
We investigate the dynamics of localized solutions of the relativistic cold fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed…
We study the evolution of a wave packet in a nonlinear Schr\"odinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue…
We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre…