Soliton molecules in trapped vector Nonlinear Schrodinger systems

We study a new class of vector solitons in trapped Nonlinear Schrodinger systems modelling the dynamics of coupled light beams in GRIN Kerr media and atomic mixtures in Bose-Einstein condensates. These solitons exist for different spatial dimensions, their existence is studied by means of a systematic mathematical technique and the analysis is made for inhomogeneous media

Stable vortex and dipole vector solitons in a saturable nonlinear medium

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.Comment: To appear in Phys. Rev.