Stable vortex and dipole vector solitons in a saturable nonlinear medium

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 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 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.

To appear in Phys. Rev. E

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• Incoherent vector vortex-mode solitons in self-focusing nonlinear media
• Composite vortex-ring solitons in Bessel photonic lattices
• Stabilized vortex solitons in layered Kerr media
• Scattering of dipole-mode vector solitons: Theory and experiment
• Similarity Solution of the 3-phase Stefan Problem for Alloys with Arbitrary Temperature Dependent Properties
• Universally-convergent Squared-operator Iteration Methods for Solitary Waves in General Nonlinear Wave Equations
• Instabilities of multi-hump vector solitons in coupled nonlinear Schroedinger equations