Unstaggered-staggered solitons in two-component discrete nonlinear Schr\"{o}dinger lattices

TL;DR

This paper introduces stable mixed unstaggered-staggered bright solitons in a two-component discrete nonlinear Schrödinger system with attractive SPM and repulsive XPM interactions, using analytical and numerical methods to analyze their stability.

Contribution

The study presents the first analytical and numerical characterization of symbiotic unstaggered-staggered solitons in coupled DNLS equations with specific nonlinear interactions.

Findings

Most symbiotic solitons are accurately predicted by the variational approximation.

The solitons are stable according to the generalized Vakhitov-Kolokolov criterion.

Near the existence boundary, broad solitons are unstable and not well approximated by VA.

Abstract

We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schr\"{o}dinger (DNLS) equations with the attractive self-phase-modulation (SPM) nonlinearity, coupled by the repulsive cross-phase-modulation (XPM) interaction. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. The results are obtained in an analytical form, using the variational and Thomas-Fermi approximations (VA and TFA), and the generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the stability. The analytical predictions are verified against numerical results. Almost all the symbiotic solitons are predicted by the VA quite accurately, and are stable. Close to a boundary of the existence region of the solitons (which may feature several connected branches), there are broad solitons which are not well approximated by the VA, and are unstable.