Stabilization of high-order solutions of the cubic nonlinear Schrödinger equation.

In this paper we consider the stabilization of nonfundamental unstable stationary solutions of the cubic nonlinear Schrödinger equation. Specifically, we study the stabilization of radially symmetric solutions with nodes and asymmetric complex stationary solutions. For the first ones, we find partial stabilization similar to that recently found for vortex solutions while for the later ones stabilization does not seem possible.

n-body dynamics of stabilized vector solitons.

In this work we study the interactions between stabilized Townes solitons. By means of effective Lagrangian methods, we have found that the interactions between these solitons are governed by central forces, in a first approximation. In our numerical simulations we describe different types of orbits, deflections, trapping, and soliton splitting.

Stabilized vortices in layered Kerr media.

In this paper, we demonstrate the possibility of stabilizing beams with angular momentum propagating in Kerr media against filamentation and collapse. Very long propagation distances can be achieved by combining the choice of an appropriate layered medium with alternating focusing and defocusing nonlinearities with the presence of an incoherent guiding beam which is itself stabilized in this medium. The applicability of the results to the field of matter waves is also discussed.

Stabilized two-dimensional vector solitons.

In this Letter, we introduce the concept of stabilized vector solitons as nonlinear waves constructed by the addition of mutually incoherent fractions of Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We analyze the stability of these new kinds of structures and describe their behavior and formation in Manakov-like interactions. Potential applications of our results in Bose-Einstein condensation and nonlinear optics are also discussed.