Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices

Abstract

It has been recently discovered that stabilization of two-dimensional (2D) solitons against the critical collapse in media with the cubic nonlinearity by means of nonlinear lattices (NLs) is a challenging problem. We address the 1D version of the problem, i.e., the nonlinear-Schrödinger equation (NLSE) with the quintic or cubic-quintic (CQ) terms, the coefficient in front of which is periodically modulated in space. The models may be realized in optics and Bose-Einstein condensates (BECs). Stability diagrams for the solitons are produced by means of numerical methods and analytical approximations. It is found that the sinusoidal NL stabilzes solitons supported by the quintic-only nonlinearity in a narrow stripe in the respective parameter plane, on the contrary to the case of the cubic nonlinearity in 2D, where the stabilization of solitons by smooth spatial modulations is not possible at all. The stability region is much broader in the 1D CQ model, where higher-order solitons may be stable too.

8 pages,9 figures. Physical Review A (in press)

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• Spontaneous symmetry breaking in a nonlinear double-well structure
• Stable two-dimensional solitons in nonlinear lattices
• Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons
• Solitary Waves Under the Competition of Linear and Nonlinear Periodic Potentials
• Bose-Einstein condensates under a spatially-modulated transverse confinement
• Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials
• One-Dimensional Bose Gases with N-Body Attractive Interactions
• Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials

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• Stability conditions for one-dimensional optical solitons in cubic-quintic-septimal media
• Gap-type dark localized modes in a Bose-Einstein condensate with optical lattices
• Bright solitons in defocusing media with spatial modulation of the quintic nonlinearity
• Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity
• One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potential
• Gaussian-like and flat-top solitons of atoms with spatially modulated repulsive interactions
• Suppression of the critical collapse for one-dimensional solitons by saturable quintic nonlinear lattices
• Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity
• Dynamical stabilization of two-dimensional trapless Bose-Einstein condensates by three-body interaction and quantum fluctuations
• Stabilization of trapless dipolar Bose-Einstein condensates by temporal modulation of the contact interaction
• Two-dimensional intra-band solitons in lattice potentials with local defects and self-focusing nonlinearity
• Asymmetric localized states in periodic potentials with a domain wall-like Kerr nonlinearity
• Self-trapped spatially localized states in combined linear-nonlinear periodic potentials