J. Yang and D.E. Pelinovsky

Stable vortex and dipole vector solitons in a saturable nonlinear medium

Phys. Rev. E 67, 016608 (2003)

Abstract:
We study both analytically and numerically the existence, uniqueness, and stability of vortex and dipole vector solitons in a saturable nonlinear medium in (2+1) dimensions. We construct perturbation series expansions for the vortex and dipole vector solitons near the bifurcation point where the vortex and dipole components are {\em small}. We show that both solutions uniquely bifurcate from the same bifurcation point. We also prove that both vortex and dipole vector solitons are linearly {\em stable} in the neighborhood of the bifurcation point. Far from the bifurcation point, the family of vortex solitons becomes linearly unstable via oscillatory instabilities, while the family of dipole solitons remains stable in the entire domain of existence. In addition, we show that an unstable vortex soliton breaks up either into a rotating dipole soliton or into two rotating fundamental solitons.

Keywords:
VORTICES, DIPOLES, PHOTOREFRACTIVE CRYSTALS, SATURABLE NONLINEAR MEDIUM, SYSTEMS OF COUPLED NONLINEAR SCHRODINGER EQUATIONS, STABILITY THEORY, PERTURBATION SERIES EXPANSIONS