FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 7, PAGES 35-63

**Multi-component vortex solutions in symmetric coupled nonlinear
Schrödinger equations**

A. S. Desyatnikov

D. E. Pelinovsky

J. Yang

Abstract

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A Hamiltonian system of incoherently coupled nonlinear
Schrödinger equations is considered in the context of physical
experiments in photorefractive crystals and Bose--Einstein
condensates.
Due to the incoherent coupling, the Hamiltonian system has
a group of various symmetries that include symmetries with
respect to gauge transformations and polarization rotations.
We show that the group of rotational symmetries generates a large
family of vortex solutions that generalize scalar vortices, vortex
pairs with either double or hidden charge and coupled states between
solitons and vortices.
Novel families of vortices with different frequencies and vortices
with different charges at the same component are constructed and their
linearized stability problem is block-diagonalized for numerical
analysis of unstable eigenvalues.

Location: http://mech.math.msu.su/~fpm/eng/k06/k067/k06703h.htm

Last modified: February 13, 2007