Nonintegrable Schrodinger Discrete Breathers

TL;DR

This paper numerically investigates nonintegrable discrete breathers in nonlinear Schrödinger lattices, revealing their structure as a localized core with a resonant wave background, and analyzes their energy dynamics.

Contribution

It introduces a numerical method to continue solutions from integrable to nonintegrable regimes and characterizes the structure and energy balance of moving discrete breathers.

Findings

Breathers consist of a localized core and a resonant wave background.

The background is essential for energy balance during motion.

Perturbative theory predictions are critically evaluated.

Abstract

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.