Related papers: Acoustic breathers in two-dimensional lattices
The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations. Following an earlier work [Comm. Math. Phys. {\bf 302},…
We study the existence and stability of multisite discrete breathers in two prototypical non-square Klein-Gordon lattices, namely a honeycomb and a hexagonal one. In the honeycomb case we consider six-site configurations and find that for…
We consider the Hamiltonian version of a $\cal PT$-symmetric lattice that describes dynamics of coupled pendula under a resonant periodic force. Using the asymptotic limit of a weak coupling between the pendula, we prove the nonlinear…
Nonlinear lattice models can support "discrete breather" excitations that stay localized in space for all time. By contrast, the localized Wannier states of linear lattice models are dynamically unstable. Nevertheless, symmetric and…
Artificial intelligence in the form of deep learning is now very popular and directly implemented in many areas of science and technology. In the present work we study time evolution of Discrete Breathers in one-dimensional nonlinear chains…
We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we…
We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay.…
The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the performed simulations demonstrate that a…
We consider the evolution of the 2-soliton (breather) of the nonlinear Schroedinger equation on a semi-infinite line with the zero boundary condition and a linear potential, which corresponds to the gravity field in the presence of a hard…
We study discrete surface breathers in two-dimensional lattices of inductively-coupled split-ring resonators with capacitive nonlinearity. We consider both Hamiltonian and dissipative systems and analyze the properties of the modes…
In the present work, we examine a prototypical model for the formation of bright breathers in nonlinear left-handed metamaterial lattices. Utilizing the paradigm of nonlinear transmission lines, we build a relevant lattice and develop a…
In this paper we study the existence and linear stability of bright and dark breathers in one-dimensional FPU lattices. On the one hand, we test the range of validity of a recent breathers existence proof [G. James, {\em C. R. Acad. Sci.…
Long-lived localized field configurations such as breathers, oscillons, or more complex objects naturally arise in the context of a wide range of nonlinear models in different numbers of spatial dimensions. We present a numerical method,…
The occurrence of single- or multisite localized vibrational modes, also called Discrete Breathers (DBs), in 2D hexagonal dusty plasma (DP) lattices is investigated. The system is described by a Klein-Gordon hexagonal lattice characterized…
In different nonlinear mediums, the wave trains carry energy and expose many amazing features. To describe a nonlinear phenomenon, a soliton is one that preserves its shape and amplitude even after the collision. Breather is one kind of…
A quasi-one-dimensional Bose-Einstein condensate loaded into a quasi-periodic potential created by two sub-lattices of comparable amplitudes and incommensurate periods is considered. Although the conventional tight-binding approximation is…
In this article we prove the existence of a new family of periodic solutions for discrete, nonlinear Schrodinger equations subject to spatially localized driving and damping. They provide an alternate description of the metastable behavior…
Exact stability analysis of 1-site breathers in an NLS type model (ref. [4], see below) indicates destabilisation through a growth rate becoming positive as a stability border is crossed, while above a critical spatial decay rate…
We consider the nonlinear Schr\"odinger equation with non-local derivatives in a two-dimensional periodic domain. For certain orders of derivatives, we find a new type of breather solution dominating the field evolution at low nonlinearity…
We study solitons arising in a system describing the interaction of a two-dimensional discrete hexagonal lattice with an additional electron field (or, in general, an exciton field). We assume that this interaction is electron-phonon-like.…