Related papers: Nonlinear breathers with crystalline symmetries
A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in 2D and 3D lattice dynamical models is developed. This approach is demonstrated for the scalar models on the plane square lattice. The…
We introduce a one dimensional parity-time (PT)-symmetric nonlinear magnetic metamaterial consisted of split ring dimers having both gain and loss. When nonlinearity is absent we find a transition between an exact to a broken PT-phase; in…
We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor,…
We investigate the interplay of nonreciprocity and nonlinearity in a one-dimensional nonlinear Klein-Gordon chain of classical oscillators coupled by asymmetric springs, akin to a mechanical analogue of the Hatano-Nelson model with onsite…
Discrete breathers with purely anharmonic short-range interaction potentials localize super-exponentially becoming compact-like. We analyze their spatial localization properties and their dynamical stability. Several branches of solutions…
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…
We touch upon the wide topic of discrete breather formation with a special emphasis on the the $\phi^4$ model. We start by introducing the model and discussing some of the application areas/motivational aspects of exploring time periodic,…
We study a discrete two-dimensional nonlinear system that allows for discrete breather solutions. We perform a spectral analysis of the lattice dynamics at thermal equilibrium and use a cooling technique to measure the amount of breathers…
Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from the prototypical example of the Fermi-Pasta-Ulam model to Klein-Gordon nonlinear lattices, among many others. We propose a general criterion for the…
We investigate the spectral properties of one-dimensional spatially modulated nonlinear phononic lattices, and their evolution as a function of amplitude. In the linear regime, the stiffness modulations define a family of periodic and…
We prove the existence of time-periodic solutions and spatially localised solutions (breathers), in general nonlinear Klein-Gordon infinite lattices. The existence problem is converted into a fixed point problem for an operator on some…
In this work, we study the dynamics of an infinite array of nonlinear dimer oscillators which are linearly coupled as in the classical model of Su, Schrieffer and Heeger (SSH). The ratio of in-cell and out-of-cell couplings of the SSH model…
Physico-mechanical properties of polymers in solid state, in particular conditions of their structural transformations, are substantially defined by existence and mobility of elementary nonlinear excitations. The localized oscillatory…
We study anharmonic localization in a periodic five atom chain with quadratic-quartic spring potential. We use discrete symmetries to eliminate the degeneracies of the harmonic chain and easily find periodic orbits. We apply linear…
Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation with positive cubic nonlinearity, which in the limits of small and large amplitudes tends to…
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 report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and traveling self-localized modes were generated experimentally and theoretically in…
Nonlinearity shapes lattice dynamics affecting vibrational spectrum, transport and thermalization phenomena. Beside breathers and solitons one finds the third fundamental class of nonlinear modes -- $q$-breathers -- periodic orbits in…
In this paper we investigate the emergence of time-periodic and and time-quasiperiodic (sometimes infinitely long lived and sometimes very long lived or metastable) solutions of discrete nonlinear wave equations: discrete sine Gordon,…
It has recently been theoretically predicted and experimentally observed that a soliton resulting from nonlinearity can be pumped across an integer or fractional number of unit cells as a system parameter is slowly varied over a pump…