Stable vortex and dipole vector solitons in a saturable nonlinear medium

Details Stable vortex and dipole vector solitons in a saturable nonlinear medium Stable vortex and dipole vector solitons in a saturable nonlinear medium

2002-12-13

arxiv.org/abs/nlin/0212034v1

Nonlinear Sciences

Pattern Formation and Solitons

To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.67.016608

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.

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