| Contents |
| The talk aims to give a review of recently obtained results which
demonstrate that defocusing cubic media with spatially inhomogeneous
nonlinearity, whose strength increases rapidly enough toward the periphery
(faster than $r^D% in the $D$-dimensional space, $D = 1,2,3$, where $r$ is the radial
coordinate), can support a variety of stable solitons in all three dimensions,
including one-dimensional (1D) fundamental and multihump states, 2D
vortex solitons with arbitrary topological charges, and vortex tori
(soliton gyroscopes) in 3D. Solitons maintain their coherence in the state
of motion, oscillating in the effective nonlinear potential as robust
quasiparticles.The 3D vortex tori exhibit stable precession, induced by the
application of external torque. In addition to numerically found soliton families,
particular solutions can be obtained in an exact analytical form, and accurate
approximations are developed for the entire families by means of the variational
and Thomas-Fermi approximations. Essentially the same mechanism for the
self-trapping of bright solitons under the action of the spatially growing
repulsive nonlinearity works in nonlocal media, and in discrete systems too.
Furthermore, related numerical and analytical results demonstrate the existence of
stable dissipative solitons in media with the uniform linear gain and nonlinear
loss, whose local strength grows toward the periphery faster than r^D. Such 1D and
2D settings can be implemented in nonlinear optics and BEC. The 3D setting may be
created in BEC. |
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