Dynamical Barrier for the Formation of Solitary Waves in Discrete Lattices

TL;DR

This paper investigates the conditions under which localized solitary waves form in nonlinear Schrödinger lattices, highlighting a dynamical barrier related to initial excitation amplitude and comparing 1D and 2D cases.

Contribution

It introduces an energetic criterion for the formation of localized modes and compares dynamics across integrable and non-integrable Schrödinger models.

Findings

Existence of a dynamical barrier for solitary wave formation.

A sufficient amplitude condition for localized mode excitation.

Differences between 1D and 2D lattice behaviors.

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 Schrodinger 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 Schrodinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schrodinger equation.