Multi-component vortices in coupled NLS equations
Abstract:
A Hamiltonian system of incoherently coupled nonlinear Schrödinger (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.