相关论文: Discrete breathers in a two-dimensional hexagonal …

We study the stability of a stationary discrete breather (DB) on a nonlinear trimer in the framework of the discrete nonlinear Schr\"odinger equation (DNLS). In previous theoretical investigations of the dynamics of Bose-Einstein…

We demonstrate that stabilization of solitons of the multidimensional Schrodinger equation with a cubic nonlinearity may be achieved by a suitable periodic control of the nonlinear term. The effect of this control is to stabilize the…

A simple model of a polymer is considered: a chain of (different) point masses, connected by harmonic springs, embedded in two dimensional space. In order to determine conditions for existence and stability of breather excitations, the…

We study the scattering of a moving discrete breather (DB) on a junction in a Fermi-Pasta-Ulam (FPU) chain consisting of two segments with different masses of the particles. We consider four distinct cases: (i) a light-heavy (abrupt)…

We investigate the connection between local and global dynamics in the Fermi -- Pasta -- Ulam (FPU) $\beta$ -- model from the point of view of stability of its simplest periodic orbits (SPOs). In particular, we show that there is a…

We consider a Hamiltonian chain of weakly coupled anharmonic oscillators. It is well known that if the coupling is weak enough then the system admits families of periodic solutions exponentially localized in space (breathers). In this paper…

We study nonlinear phonon excitations in a one-dimensional quantum nonlinear lattice model using numerical exact diagonalization. We find that multi-phonon bound states exist as eigenstates which are natural counterparts of breather…

We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal…

In this paper, we prove existence and uniqueness of solutions to the Fermi Pasta Ulam lattice equation that converge to a sum of co-propagating $N$ solitary waves as $t\to\infty$ using linear stability property of multi-soliton like…

We explore dynamics of discrete breathers and multi-breathers in finite one-dimensional chain. The model involves parabolic on-site potential with rigid constraints and linear nearest-neighbor coupling. The rigid non-ideal impact…

We explore the dynamics of strongly localized periodic solutions (discrete solitons, or discrete breathers) in a finite one-dimensional chain of asymmetric vibro-impact oscillators. The model involves a parabolic on-site potential with…

We prove global existence and uniqueness of solutions of some important nonlinear lattices which include the Fermi-Pasta-Ulam (FPU) lattice. Our result shows (on a particular example) that the FPU lattice with high nonlinearity and its…

We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is…

We consider the static wall approximation to the dynamics of a particle bouncing on a periodically oscillating infinitely heavy plate while subject to a potential force. We assume the case of a potential given by a power of the particle's…

The dynamics of energy relaxation in thermalized one- and two-dimensional arrays with nonlinear interactions depend in detail on the interactions and, in some cases, on dimensionality. We describe and explain these differences for arrays of…

We discuss the process by which energy, initially evenly distributed in a nonlinear lattice, can localize itself into large amplitude excitations. We show that, the standard modulational instability mechanism, which can initiate the process…

We investigate, both analytically and numerically, dispersive fractalization and quantization of solutions to periodic linear and nonlinear Fermi-Pasta-Ulam-Tsingou systems. When subject to periodic boundary conditions and discontinuous…

We show that the two-dimensional, nonlinear Schr\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give…

The Fermi-Pasta-Ulam (FPU) chains of particles in \textit{thermal equilibrium} are studied from both wave-interaction and particle-interaction points of view. It is shown that, even in a strongly nonlinear regime, the chain in thermal…

Discrete breathers (nonlinear localised modes) have been shown to exist in various nonlinear Hamiltonian lattice systems. In the present paper we study the dynamics of classical spins interacting via Heisenberg exchange on spatial…