Interlaced solitons and vortices in coupled DNLS lattices

TL;DR

This paper introduces interlaced solitons and vortices in coupled nonlinear lattices, analyzing their existence, stability, and dynamics through theoretical and numerical methods in one and higher dimensions.

Contribution

It presents a new class of coherent structures called interlaced solitons in multi-component nonlinear lattices, with systematic stability analysis and numerical simulations.

Findings

Stable interlaced solitons can be constructed from unary patterns.

Analytical stability results in 1D; numerical in higher dimensions.

Unstable structures break into simpler configurations.

Abstract

In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one components, namely interlaced solitons. These are waveforms in which in the relevant anti-continuum limit, i.e. when the sites are uncoupled, one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create ones such for the binary case of two-components. In the one-dimensional setting, we provide also a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort to corresponding numerical computations. Lastly, we perform direct numerical simulations to showcase how these structures break up, when exponentially or oscillatorily unstable, to structures with a smaller number of participating sites.