Journal ArticleDOI
On a class of discretizations of Hamiltonian nonlinear partial differential equations
TLDR
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.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 2003-09-01. It has received 60 citations till now. The article focuses on the topics: Multigrid method & Nonlinear system.read more
Citations
More filters
Journal ArticleDOI
Non-standard Hubbard models in optical lattices: a review
Omjyoti Dutta,Mariusz Gajda,Philipp Hauke,Philipp Hauke,Maciej Lewenstein,Dirk-Sören Lühmann,Boris A. Malomed,Tomasz Sowiński,Jakub Zakrzewski +8 more
TL;DR: The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation for the original physical Hamiltonian, and the effects related to higher Bloch bands also become important even for deep optical lattices.
Book
Localization in Periodic Potentials: From Schrodinger Operators to the Gross-Pitaevskii Equation
TL;DR: In this paper, the authors provide a comprehensive treatment of the Gross-Pitaevskii equation with a periodic potential; in particular, the localized modes supported by the periodic potential.
Journal ArticleDOI
Non-linear waves in lattices: past, present, future
TL;DR: In this paper, a brief summary of various areas where non-linear waves have been emerging in the phenomenology of lattice dynamical systems is presented, including nonlinear optics, atomic physics, mechanical systems, electrical lattices, nonlinear metamaterials, plasma dynamics and granular crystals.
Journal ArticleDOI
Multistable Solitons in Higher-Dimensional Cubic-Quintic Nonlinear Schrödinger Lattices
TL;DR: In this paper, the existence, stability, and mobility of fundamental discrete solitons in two-and three-dimensional nonlinear Schrodinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities were investigated.
Journal ArticleDOI
Translationally invariant nonlinear Schrödinger lattices
TL;DR: In this paper, the persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation is addressed.
References
More filters
Book
Theory of Dislocations
John Price Hirth,Jens Lothe +1 more
TL;DR: Dislocations in Isotropic Continua: Effects of Crystal Structure on Dislocations and Dislocation-Point-Defect Interactions at Finite temperatures.
Book
Solitons and the Inverse Scattering Transform
Mark J. Ablowitz,Harvey Segur +1 more
TL;DR: In this paper, the authors developed the theory of the inverse scattering transform (IST) for ocean wave evolution, which can be solved exactly by the soliton solution of the Korteweg-deVries equation.
Book
Solitons and Nonlinear Wave Equations
TL;DR: A discussion of the theory and applications of classical solitons is presented in this paper with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory, including solitary waves and soliton, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation.
BookDOI
The nonlinear Schrödinger equation : self-focusing and wave collapse
TL;DR: In this article, the authors present a basic framework to understand structural properties and long-time behavior of standing wave solutions and their relationship to a mean field generation and acoustic wave coupling.
Journal ArticleDOI
Intrinsic Localized Modes in Anharmonic Crystals
A. J. Sievers,Shozo Takeno +1 more
TL;DR: L'apparition d'un nouveau mode localise dans un reseau anharmonique pur est predite, mais possede une energie d'activation plus faible.