Solitons supported by singular spatial modulation of the Kerr nonlinearity
arXiv:1202.3813 · doi:10.1103/PhysRevA.85.023845
Abstract
We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the uniform self-defocusing (SDF) nonlinear background, and with a similar singular repulsive linear potential. The setting, which can be implemented in optics and BEC, aims to extend the general analysis of the existence and stability of solitons in NLSEs. Results for fundamental solitons are obtained analytically and verified numerically. The solitons feature a quasi-cuspon shape, with the second derivative diverging at the center, and are stable in the entire existence range, which is 0 < a < 1. Dipole (odd) solitons are found too. They are unstable in the infinite domain, but stable in the semi-infinite one. In the presence of the SDF background, there are two subfamilies of fundamental solitons, one stable and one unstable, which exist together above a threshold value of the norm (total power of the soliton). The system which additionally includes the singular repulsive linear potential emulates solitons in a uniform space of the fractional dimension, 0 < D < 1. A two-dimensional extension of the system, based on the quadratic nonlinearity, is formulated too.
Physical Review A, in press
References in corpus (15)
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
- Spontaneous symmetry breaking in a nonlinear double-well structure
- Bright solitons from defocusing nonlinearities
- Algebraic bright and vortex solitons in defocusing media
- Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices
- Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity
- Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices
- Solitons supported by localized nonlinearities in periodic media
- Matter-wave solitons with a periodic, piecewise-constant nonlinearity
- Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates
- Self-trapping and splitting of bright vector solitons under inhomogeneous defocusing nonlinearities
- Interlaced linear-nonlinear optical waveguide arrays
- Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials
- Quantum phase transition of Bose-Einstein condensates on a ring nonlinear lattice
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- Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity