Mobile Localization in nonlinear Schrodinger lattices

TL;DR

This paper investigates mobile discrete breathers in the nonlinear Schrödinger lattice, revealing that background plane waves are essential for mobility away from integrability, balancing energy variations during motion.

Contribution

It demonstrates the role of resonant plane wave backgrounds in enabling mobile localization in non-integrable discrete nonlinear Schrödinger lattices.

Findings

Mobile breathers are supported by a background of resonant plane waves.

The background is crucial for maintaining localization during motion.

Energy variations are balanced by interactions with the background.

Abstract

Using continuation methods from the integrable Ablowitz-Ladik lattice, we have studied the structure of numerically exact mobile discrete breathers in the standard Discrete Nonlinear Schrodinger equation. We show that, away from that integrable limit, the mobile pulse is dressed by a background of resonant plane waves with wavevectors given by a certain selection rule. This background is seen to be essential for supporting mobile localization in the absence of integrability. We show how the variations of the localized pulse energy during its motion are balanced by the interaction with this background, allowing the localization mobility along the lattice.