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Related papers: Discrete breathers in $\phi^4$ and related models

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Existence of large-amplitude time-periodic breathers localized near a single site is proved for the discrete Klein--Gordon equation, in the case when the derivative of the on-site potential has a compact support. Breathers are obtained at…

Pattern Formation and Solitons · Physics 2010-11-30 Guillaume James , Dmitry Pelinovsky

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…

High Energy Physics - Theory · Physics 2009-10-31 M. Haskins , J. M. Speight

We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Nonlinearity {\bf 12}, 1373 (1999) and Phys. Rev. E {\bf 72}, 035602(R) (2005), such that they support not only kinks but a…

Pattern Formation and Solitons · Physics 2009-11-11 S. V. Dmitriev , P. G. Kevrekidis , N. Yoshikawa , D. J. Frantzeskakis

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…

Statistical Mechanics · Physics 2009-11-10 Maria Eleftheriou , Sergej Flach

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…

Pattern Formation and Solitons · Physics 2007-05-23 Michael Kastner , Tomas J. Lazaro

It is demonstrated that the breather solutions recently discovered in the weakly coupled topological discrete sine-Gordon system are spectrally unstable. This is in contrast with more conventional spatially discrete systems, whose breathers…

High Energy Physics - Theory · Physics 2014-11-12 J. M. Speight

We study metastable behavior in a discrete nonlinear Schr\"odinger equation from the viewpoint of Hamiltonian systems theory. When there are $n < \infty$ sites in this equation, we consider initial conditions in which almost all the energy…

Dynamical Systems · Mathematics 2020-10-28 Jean-Pierre Eckmann , C. Eugene Wayne

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…

Pattern Formation and Solitons · Physics 2023-06-07 A. Hofstrand , H. Li , M. I. Weinstein

We examine the dynamics of strongly localized periodic solutions (discrete breathers) in two-dimensional array of coupled finite one-dimensional chains of oscillators. Localization patterns with both single and multiple localization sites…

Pattern Formation and Solitons · Physics 2017-05-18 Itay Grinberg , Oleg V. Gendelman

This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain-hardening and strain-softening. The existence, stability, and bifurcation…

Pattern Formation and Solitons · Physics 2023-05-24 Marisa M. Lee , Efstathios G. Charalampidis , Siyuan Xing , Christopher Chong , Panayotis G. Kevrekidis

In the present work, we revisit the highly active research area of inhomogeneously nonlinear defocusing media and consider the existence, spectral stability and nonlinear dynamics of bright solitary waves in them. We use the anti-continuum…

Pattern Formation and Solitons · Physics 2015-09-02 P. G. Kevrekidis , R. L. Horne , N. Whitaker , Q. E. Hoq , D. Kip

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. An important issue, not only from a theoretical point of view but also for…

Pattern Formation and Solitons · Physics 2009-11-10 Michael Kastner

We study deterministic escape dynamics in the framework of the discrete Klein-Gordon modelwith a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and…

Pattern Formation and Solitons · Physics 2015-05-20 V. Achilleos , A. Álvarez , J. Cuevas , D. J. Frantzeskakis , N. I. Karachalios , P. G. Kevrekidis , B. Sánchez-Rey

Deflation is an efficient numerical technique for identifying new branches of steady state solutions to nonlinear partial differential equations. Here, we demonstrate how to extend deflation to discover new periodic orbits in nonlinear…

Pattern Formation and Solitons · Physics 2023-05-30 F. Martin-Vergara , J. Cuevas-Maraver , P. E. Farrell , F. R. Villatoro , P. G. Kevrekidis

By applying an out-of-phase actuation at the boundaries of a uniform chain of granular particles, we demonstrate experimentally that time-periodic and spatially localized structures with a nonzero background (so-called dark breathers)…

Pattern Formation and Solitons · Physics 2015-06-16 C. Chong , F. Li , J. Yang , M. O. Williams , I. G. Kevrekidis , P. G. Kevrekidis , C. Daraio

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…

Pattern Formation and Solitons · Physics 2018-02-14 V. Koukouloyannis , P. G. Kevrekidis , G. P. Veldes , D. J. Frantzeskakis , D. DiMarzio , X. Lan , V. Radisic

We derive a Hamiltonian version of the ${\cal PT}$-symmetric discrete nonlinear Schr\"{o}dinger equation that describes synchronized dynamics of coupled pendula driven by a periodic movement of their common strings. In the limit of weak…

Mathematical Physics · Physics 2016-05-23 Alexander Chernyavsky , Dmitry E. Pelinovsky

We discuss the interplay between a slow continuous drift of temperature, which induces continuous phase separation, and the non-linear diffusion term in the $\phi^4$-model for phase separation of a binary mixture. This leads to a bound for…

Statistical Mechanics · Physics 2012-05-31 Juergen Vollmer

The existence, stability and movability of breathers in a model for alpha-helix proteins is studied. This model basically consists a chain of dipole moments parallel to it. The existence of localized linear modes brings about that the…

Pattern Formation and Solitons · Physics 2009-11-07 J. F. R. Archilla , Yu B. Gaididei , P. L. Christiansen , J. Cuevas

In the present work, we consider a variety of two-component, one-dimensional states in nonlinear Schrodinger equations in the presence of a parabolic trap, inspired by the atomic physics context of Bose-Einstein condensates. The use of…

Pattern Formation and Solitons · Physics 2017-06-28 Haitao Xu , Panayotis G. Kevrekidis , Todd Kapitula