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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Modulational and numerical solutions for the steady discrete Sine–Gordon equation in two space dimensions
TL;DR: In this article, a modulation theory based on a suitably averaged Lagrangian for steady solutions of the Sine-Gordon equation in a two-dimensional lattice is developed, which gives approximate solutions away from small perturbations of the exact anti-continuum solutions for both radial and polygonal solutions.
Posted Content
Stationary multi-kinks in the discrete sine-Gordon equation
TL;DR: In this article, the existence and spectral stability of static multi-kink structures in the discrete sine-Gordon equation, as a representative example of the family of discrete Klein-Gordon models, were investigated.
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Jog my shape memory: dynamics as a challenge in mathematical materials science.
TL;DR: This review discusses some aspects of a multiscale analysis of martensitic materials as a prominent example of materials that exhibit nuanced structures and surprising implications on various scales.
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Transient radiative behavior of Hamiltonian systems in finite domains
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Discrete Solitary Waves in Systems with Nonlocal Interactions and the Peierls-Nabarro Barrier
TL;DR: In this paper, a class of discrete focusing nonlinear Schr{o}dinger equations (DNLS) with general nonlocal interactions was studied and the existence of onsite and offsite discrete solitary waves, which bifurcate from the trivial solution at the endpoint frequency of the continuous spectrum of linear dispersive waves, was shown.
References
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Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
Book
Applications of Centre Manifold Theory
TL;DR: In this paper, the authors present an approach for solving the panel flutter problem using a Second Order Equation (SOPE) and a Semigroup Theory. But their approach is limited to the case when the case is 1 < 0 and the case where 0 < 0.
Journal ArticleDOI
Discrete Spatial Optical Solitons in Waveguide Arrays
TL;DR: In this paper, the authors reported the observation of discrete spatial optical solitons in an array of 41 waveguides, where light was coupled to the central waveguide and when sufficient power was injected, the field was localized close to the input waveguiders and its distribution was successfully described by the discrete nonlinear Schrodinger equation.
Book
Topics in Nonlinear Functional Analysis
TL;DR: Topological approach: Finite dimensions Topological degree in Banach space Bifurcation theory Further topological methods Monotone operators and the min-max theorem Generalized implicit function theorems Bibliography as mentioned in this paper
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