Dynamical barrier for the formation of solitary waves in discrete lattices

Academic Article

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. © 2007 Elsevier B.V. All rights reserved.
  • Digital Object Identifier (doi)

    Author List

  • Kevrekidis PG; Espinola-Rocha JA; Drossinos Y; Stefanov A
  • Start Page

  • 2247
  • End Page

  • 2253
  • Volume

  • 372
  • Issue

  • 13