Spatial control of the competition between self-focusing and self-defocusing nonlinearities in one- and two-dimensional systems

Abstract

We introduce a system with competing self-focusing (SF) and self-defocusing (SDF) terms, which have the same scaling dimension. In the one-dimensional (1D) system, this setting is provided by a combination of the SF cubic term multiplied by the delta-function, $\delta (x)$, and a spatially uniform SDF quintic term. This system gives rise to the most general family of 1D-Townes solitons, the entire family being unstable. However, it is completely stabilized by a finite-width regularization of the $\delta$-function. The results are produced by means of numerical and analytical methods. We also consider the system with a symmetric pair of regularized $\delta$-functions, which gives rise to a wealth of symmetric, antisymmetric, and asymmetric solitons, linked by a bifurcation loop, that accounts for the breaking and restoration of the symmetry. Soliton families in 2D versions of both the single- and double-delta-functional systems are also studied. The 1D and 2D settings may be realized for spatial solitons in optics, and in Bose-Einstein condensates.

19 pages, 22 figures

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• Theory of ultracold Fermi gases
• Controlling a magnetic Feshbach resonance with laser light
• Spontaneous symmetry breaking in a nonlinear double-well structure
• Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity
• One-Dimensional Bose Gases with N-Body Attractive Interactions