Dynamics of lattice kinks
TLDR
In this paper, the authors consider a class of Hamiltonian nonlinear wave equations governing a field defined on a spatially discrete one-dimensional lattice, with discreteness parameter, d = h −1, where h > 0 is the lattice spacing.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 2000-08-01 and is currently open access. It has received 51 citations till now. The article focuses on the topics: Breather & Phase portrait.read more
Citations
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The discrete nonlinear schrödinger equation: a survey of recent results
TL;DR: In this paper, a review of recent developments in the study of the Discrete Nonlinear Schrodinger (DNLS) equation is presented in one and two spatial dimensions, concerning ground and excited states, their construction, stability and bifurcations.
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Selection of the ground state for nonlinear schrödinger equations
TL;DR: In this paper, a class of nonlinear Schrodinger systems (NLS) having two nonlinear bound states was studied and the authors showed that the general large time behavior is characterized by decay of the excited state, asymptotic approach to the nonlinear ground state and dispersive radiation.
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Selection of the ground state for nonlinear Schroedinger equations
Avy Soffer,Michael I. Weinstein +1 more
TL;DR: In this article, a class of nonlinear Schr\"odinger systems (NLS) having two nonlinear bound states was studied and the authors showed that the general large time behavior is characterized by decay of the excited state, asymptotic approach to the nonlinear ground state and dispersive radiation.
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On a class of discretizations of Hamiltonian nonlinear partial differential equations
TL;DR: In this article, a new class of discretizations of partial differential equations (PDEs) that preserve a (momentum-like) integral of the motion is presented, which results in an effective translational invariance for the dynamical problem and the absence of a Peierls-Nabarro barrier.
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Discrete Klein–Gordon models with static kinks free of the Peierls–Nabarro potential
TL;DR: For the nonlinear Klein-Gordon type models, a general method of discretization was proposed in this article in which the static kink can be placed anywhere with respect to the lattice.
References
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Kink dynamics in the highly discrete sine-Gordon system
Michel Peyrard,Martin D. Kruskal +1 more
TL;DR: In this article, the authors studied kink dynamics in a very discrete sine-Gordon system where the kink width is of the order of the lattice spacing and showed that kinks lose the memory of their initial velocity and propagate preferentially at well-defined velocities which correspond to quasi-steady states.
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Dynamics of Discrete Solitons in Optical Waveguide Arrays
TL;DR: In this article, the effect of the Peierls-Nabarro potential has been observed in a macroscopic system with discrete solitons, where the initial excitation is not centered on a waveguide.
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Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit
Gero Friesecke,Robert L. Pego +1 more
TL;DR: In this article, it was shown that for speeds close to sonic, unique single-pulse waves exist and the profiles are governed by a continuum limit valid on all length scales, not just the scales suggested by formal asymptotic analysis.
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Critical behaviour at the transition by breaking of analyticity in the discrete Frenkel-Kontorova model
Michel Peyrard,Serge Aubry +1 more
TL;DR: In this article, the authors study the transition by breaking of analyticity which occurs in the incommensurate ground state of the Frenkel-Kontorova model (1938) when the amplitude lambda of its periodic-potential V(u) is increased beyond a critical value lambda c. They consider four quantities which are critical when lambda goes to lambda c from upper values: the gap in the phonon spectrum, the coherence length of the ground state, the Peierls-Nabarro barrier and the depinning force.
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Excitation thresholds for nonlinear localized modes on lattices
TL;DR: In this paper, the authors consider spatially localized and time periodic solutions to discrete extended Hamiltonian dynamical systems (coupled systems of infinitely many "oscillators" which conserve total energy).
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