Stable vortex and dipole vector solitons in a saturable nonlinear medium

摘要

We study both analytically and numerically the existence, uniqueness, andstability of vortex and dipole vector solitons in a saturable nonlinear mediumin (2+1) dimensions. We construct perturbation series expansions for the vortexand dipole vector solitons near the bifurcation point where the vortex anddipole components are small. We show that both solutions uniquely bifurcatefrom the same bifurcation point. We also prove that both vortex and dipolevector solitons are linearly stable in the neighborhood of the bifurcationpoint. Far from the bifurcation point, the family of vortex solitons becomeslinearly unstable via oscillatory instabilities, while the family of dipolesolitons remains stable in the entire domain of existence. In addition, we showthat an unstable vortex soliton breaks up either into a rotating dipole solitonor into two rotating fundamental solitons.