A.S. Desyatnikov, D.E. Pelinovsky, and J. Yang
Multi-component vortex solutions in symmetrically coupled nonlinear Schrodinger equations
Journal of Mathematical Sciences 151, 3091-3111 (2008)
[Russian edition:
Fundamental'naya i Prikladnaya Matematika (Fundamental and Applied Mathematics) 12, 35-63 (2006)]
Abstract:
A Hamiltonian system of incoherently coupled nonlinear
Schrodinger (NLS) 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.
Keywords:
COUPLED NONLINEAR SCHRODINGER EQUATIONS,
SOLITONS AND VORTICES, EXISTENCE, SPECTRAL STABILITY,
ROTATIONAL SYMMETRIES, GAUGE INVARIANCE