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