Intrinsic localized modes in coupled DNLS equations from the anti-continuum limit

TL;DR

This paper extends the study of intrinsic localized modes from single-component to two-component discrete nonlinear Schrödinger systems, analyzing their existence, stability, and eigenvalue behavior through analytical and numerical methods.

Contribution

It introduces a comprehensive analysis of localized modes in two-component systems, including stability criteria and eigenvalue dependence, expanding prior single-component models.

Findings

Modes with adjacent nodes in the same phase are unstable.

Out-of-phase configurations between components can be linearly stable.

Eigenvalue analysis predicts stability regions for different mode configurations.

Abstract

In the present work, we generalize earlier considerations for intrinsic localized modes consisting of a few excited sites, as developed in the one-component discrete nonlinear Schrodinger equation model, to the case of two-component systems. We consider all the different combinations of "up" (zero phase) and "down" ({\pi} phase) site excitations and are able to compute not only the corresponding existence curves, but also the eigenvalue dependences of the small eigenvalues potentially responsible for instabilities, as a function of the nonlinear parameters of the model representing the self/cross phase modulation in optics and the scattering length ratios in the case of matter waves in optical lattices. We corroborate these analytical predictions by means of direct numerical computations. We infer that all the modes which bear two adjacent nodes with the same phase are unstable in the two component case and the only solutions that may be linear stable are ones where each set of adjacent nodes, in each component is out of phase.