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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
* discrete nonlinear Schrödinger equations * vortices * persistence and stability * Lyapunov–Schmidt reductions
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Discrete Vector On-Site Vortices, Pg Kevrekidis
Discrete Vector On-Site Vortices, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We study discrete vortices in coupled discrete nonlinear Schrödinger 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 …