相关论文: Breather interactions in the integrable discrete M…

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic,…

We study beating solitons and their interaction for the three-component nonlinear Schr\"odinger equations (NLSEs) in both focusing and defocusing cases. We identify a previously unknown family of beating solitons with nonzero relative…

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…

We report the creation of quasi-1D excited matter-wave solitons, "breathers", by quenching the strength of the interactions in a Bose-Einstein condensate with attractive interactions. We characterize the resulting breathing dynamics and…

In this paper a Frenkel--Kontorova model with a nonlinear interaction potential is used to describe a vacancy defect in a crystal. According to recent numerical results [Cuevas et al, Phys. Lett. A 315, 364 (2003)] the vacancy can migrate…

In the present chapter, we explore the possibility of a Frenkel-Kontorova (discrete sine-Gordon) model to bear interactions that decay algebraically with space, inspired by the continuum limit of the corresponding fractional derivative. In…

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…

Inspired by the recent discovery of breathing kagome materials \(\rm Nb_3Cl_8\) and \(\rm Nb_3TeCl_7\), we have explored the influence of the breathing effect on the Hubbard model of the kagome lattice. Utilizing the determinant quantum…

We investigate a quasi-1D crystal: 2D system of coupled linear chains of particles with strong intra-chain and weak inter-chain interactions. Nonlinear dynamics of one of these chains when the rest of them are fixed is reduced to the well…

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 observe dark and bright intrinsic localized modes (ILMs) or discrete breathers (DB) experimentally and numerically in a diatomic-like electrical lattice. The generation of dark ILMs by driving a dissipative lattice with…

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems…

We report the experimental observation of discrete breathers in a one-dimensional diatomic granular crystal composed of compressed elastic beads that interact via Hertzian contact. We first characterize their effective linear spectrum both…

Yang-Baxter integrable vertex models with a generic $\mathbb{Z}_2$-staggering can be expressed in terms of composite $\mathbb{R}$-matrices given in terms of the elementary $R$-matrices. Similarly, integrable open boundary conditions can be…

Motivated by recent experimental results, we study beating dark-dark solitons as a prototypical coherent structure that emerges in two-component Bose-Einstein condensates. We showcase their connection to dark- bright solitons via SO(2)…

We study theoretically the existence of bulk and surface discrete breathers in a one-dimensional magnetic metamaterial comprised of a periodic binary array of split-ring resonators. The two types of resonators differ in the size of their…

We consider the existence and spectral stability of multi-breather structures in the discrete Klein-Gordon equation, both for soft and hard symmetric potentials. To obtain analytical results, we project the system onto a finite-dimensional…

The statics, stability and dynamical properties of dark-bright soliton pairs are investigated motivated by applications in a homogeneous system of two-component repulsively interacting Bose-Einstein condensate. One of the intra-species…

Discrete breathers, or intrinsic localized modes, are spatially localized, time--periodic, nonlinear excitations that can exist and propagate in systems of coupled dynamical units. Recently, some experiments show the sighting of a form of…

We study the effects of electron-lattice interaction in the presence of discrete breathers. The lattice is treated classically. We consider two different situations - i) the scattering of an electron by a discrete breather in the…