Nonintegrable Schrodinger Discrete Breathers
  In an extensive numerical investigation of nonintegrable translational motion of discrete breathers in nonlinear Schrodinger lattices, we have used a regularized Newton algorithm to continue these solutions from the limit of the integrable Ablowitz-Ladik lattice. These solutions are shown to be a superposition of a localized moving core and an excited extended state (background) to which the localized moving pulse is spatially asymptotic. The background is a linear combination of small amplitude nonlinear resonant plane waves and it plays an essential role in the energy balance governing the translational motion of the localized core. Perturbative collective variable theory predictions are critically analyzed in the light of the numerical results. 
J. Gomez-Gardenes, L.M. Floria, M. Peyrard and A.R. Bishop