Localization phenomena in Nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates
arXiv:0804.2730 · doi:10.1016/j.physd.2008.08.020
Abstract
We study the properties of the ground state of Nonlinear Schrödinger Equations with spatially inhomogeneous interactions and show that it experiences a strong localization on the spatial region where the interactions vanish. At the same time, tunneling to regions with positive values of the interactions is strongly supressed by the nonlinear interactions and as the number of particles is increased it saturates in the region of finite interaction values. The chemical potential has a cutoff value in these systems and thus takes values on a finite interval. The applicability of the phenomenon to Bose-Einstein condensates is discussed in detail.
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- Solitons supported by spatially inhomogeneous nonlinear losses
- Localization of collisionally inhomogeneous condensates in a bichromatic optical lattice
- Solitons supported by singular spatial modulation of the Kerr nonlinearity
- Solitons and vortices in nonlinear potential wells
- Quasi-one-dimensional Bose-Einstein condensates in nonlinear lattices
- Collisional-inhomogeneity-induced generation of matter-wave dark solitons
- Effects of spatially inhomogeneous atomic interactions on Bose-Einstein condensates in optical lattices
- Stable dipole solitons and soliton complexes in the nonlinear Schrodinger equation with periodically modulated nonlinearity
- Transfer and scattering of wave packets by a nonlinear trap
- Exact solutions for periodic and solitary matter waves in nonlinear lattices
- Localized Analytical Solutions and Parameters Analysis in the Nonlinear Dispersive Gross-Pitaevskii Mean-Field GP (m,n) Model with Space-Modulated Nonlinearity and Potential