Publication Date
2008
Journal or Book Title
PHYSICS LETTERS A
Abstract
We consider the problem of the existence of a dynamical barrier of “mass” that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schrödinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schrödinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schrödinger equation.
Pages
2247-2253
Volume
372
Issue
13
Recommended Citation
Kevrekidis, PG; Espinola-Rocha, JA; Drossinos, Y; and Stefanov, A, "Dynamical barrier for the formation of solitary waves in discrete lattices" (2008). PHYSICS LETTERS A. 91.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/91
Comments
This is the prepublished version harvested from ArXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-4R5DYXB-3&_user=1516330&_coverDate=03%2F24%2F2008&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=e830a49c4fc56cb436424c2afc5049ec&searchtype=a