 Extended nonlinear waves in multidimensional dynamical latticesQ.E. Hoq, J. Gagnon, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis and R. Carretero-González Mathematics and Computers in Simulation (MATCOM), 2009, vol. 80, issue 4, 721-731 Abstract: We explore spatially extended dynamical states in the discrete nonlinear Schrödinger lattice in two- and three-dimensions, starting from the anti-continuum limit. We first consider the “core” of the relevant states (either a two-dimensional “tile” or a three-dimensional “stone”), and examine its stability analytically. The predictions are corroborated by numerical results. When the core is stable, we propose a method allowing the extension of the structure to as many sites as may be desired. In this way, various patterns of excited sites can be formed. The stability of the full extended nonlinear structures is studied numerically, which yields instability thresholds for such structures, which are attained with the increase of the lattice coupling constant. Finally, in cases of instability, direct numerical simulations are used to elucidate the evolution of the pattern; it is found that, typically, the unstable extended nonlinear pattern breaks up in an oscillatory way, leading to “lattice turbulence”. Keywords: Nonlinear lattices; Discrete solitons; Nonlinear Schrödinger equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2009:i:4:p:721-731 DOI: 10.1016/j.matcom.2009.08.035 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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