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.
Journal ArticleDOI
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.
Journal ArticleDOI
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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Motion of a Frenkel-Kontorowa Dislocation in a One-Dimensional Crystal
W. Atkinson,N. Cabrera +1 more
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Stability theory for solitary-wave solutions of scalar field equations
TL;DR: In this article, stability and instability theorems for solitary-wave solutions of classical scalar field equations were proved for the case of scalar scalar fields with singularity.
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Localized breather-like solution in a discrete Klein-Gordon model and application to DNA
TL;DR: In this paper, a discrete one-dimensional system with the 2-3 power onsite potential was studied, and the authors derived an approximate oscillating solution with a quasi-infinite lifetime.
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Single-kink dynamics in a one-dimensional atomic chain: A nonlinear atomistic theory and numerical simulation
J. Andrew Combs,Sidney Yip +1 more
TL;DR: In this article, a nonlinear lattice-dynamical theory of single kinks is presented which involves a simple equation of constraint, and a set of coupled equations of motion is derived for the kink and discrete lattice fluctuations, which retains the full details of their mutual interaction.
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