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.

KEVREKIDIS P. G.;  ESPINOLA-ROCHA J. A.;  DROSSINOS Ioannis;  STEFANOV A.; 

2008-09-22

ELSEVIER SCIENCE BV

JRC42718

0375-9601,   

http://dx.doi.org/10.1016/j.physleta.2007.11.029,    https://publications.jrc.ec.europa.eu/repository/handle/JRC42718,   

10.1016/j.physleta.2007.11.029,