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Discrete vector on-site vortices

P. G. Kevrekidis·D. E. Pelinovsky
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Abstract

We study discrete vortices in coupled discrete nonlinear Schrodinger equations. We focus on the vortex cross configuration that has been experimentally observed in photorefractive crystals. Stability of the single-component vortex cross in the anti-continuum limit of small coupling between lattice nodes is proved. In the vector case, we consider two coupled configurations of vortex crosses, namely the charge-one vortex in one component coupled in the other component to either the charge-one vortex (forming a double-charge vortex) or the charge-negative-one vortex (forming a, so-called, hidden-charge vortex). We show that both vortex configurations are stable in the anti-continuum limit if the parameter for the inter-component coupling is small and both of them are unstable when the coupling parameter is large. In the marginal case of the discrete two-dimensional Manakov system, the double-charge vortex is stable while the hidden-charge vortex is linearly unstable. Analytical predictions are corroborated with numerical observations that show good agreement near the anti-continuum limit but gradually deviate for larger couplings between the lattice nodes.

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P. G. Kevrekidis, D. E. Pelinovsky. 2005-11-23. Discrete vector on-site vortices. https://doi.org/10.1098/rspa.2006.1693

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