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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Dissertation
Localised excitations in long Josephson junctions with phase-shifts with time-varying drive
TL;DR: In this article, the authors considered a variety of ac-driven, inhomogeneous sine-Gordon equations describing an infinitely long Josephson junction with phase shifts, driven by a microwave field.
Journal ArticleDOI
On the bifurcation to moving fronts in discrete systems
TL;DR: In this article, the authors consider two model systems: a chain of coupled Lorenz equations, and a discretized Fitz?Hugh?Nagumo model, and explore how this bifurcation is modified when the systems are made spatially discrete.
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Stability of solitary waves in finite Ablowitz-Ladik lattices
TL;DR: In this paper, the effects of different types of boundary conditions on the linear stability of a solitary wave in a finite-length dynamical lattice described by the Ablowitz-Ladik (AL) model are discussed.
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Asymptotics for Supersonic Soliton Propagation in the Toda Lattice Equation
TL;DR: In this paper, a modulation theory based on the averaged Lagrangian of the discrete Toda equation was developed to explain the evolution of a supersonic soliton in the presence of impurities.
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Pseudolocalized three-dimensional solitary waves as quasi-particles
TL;DR: In this paper, a higher-order dispersive equation is introduced as a candidate for the governing equation of a field theory, and a new class of solutions of the three-dimensional field equation are considered, which are not localized functions in the sense of the integrability of the square of the profile over an infinite domain.
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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