Localized modes in the Gross-Pitaevskii equation with a parabolic trapping potential and a nonlinear lattice pseudopotential

•Nonlinear periodic lattice pseudopotential leads to new families of solutions.•Explicit asymptotic expressions for nonlinear modes in a rapidly oscillating pseudopotential.•Enhanced stability of nonlinear modes in the pseudopotential with zero mean. We study localized modes (LMs) of the one-dimensi...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2019-01, Vol.66, p.194-207
Main Authors: Alfimov, G.L., Gegel, L.A., Lebedev, M.E., Malomed, B.A., Zezyulin, D.A.
Format: Article
Language:English
Subjects:
Biological evolution
Collisionally inhomogeneous Bose–Einstein condensates
Confining
Cubic lattice
Gross-Pitaevskii equation
Lattice vibration
Magnetic resonance
Nonlinear equations
Nonlinear lattice
Nonlinearity
Optical lattices
Phase transitions
Quantum physics
Schrodinger equation
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Summary:•Nonlinear periodic lattice pseudopotential leads to new families of solutions.•Explicit asymptotic expressions for nonlinear modes in a rapidly oscillating pseudopotential.•Enhanced stability of nonlinear modes in the pseudopotential with zero mean. We study localized modes (LMs) of the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a harmonic-oscillator (parabolic) confining potential, and a periodically modulated coefficient in front of the cubic term (nonlinear lattice pseudopotential). The equation applies to a cigar-shaped Bose-Einstein condensate loaded in the combination of a magnetic trap and an optical lattice which induces the periodic pseudopotential via the Feshbach resonance. Families of stable LMs in the model feature specific properties which result from the interplay between spatial scales introduced by the parabolic trap and the period of the nonlinear pseudopotential. Asymptotic results for the shapes and stability of LMs are obtained for small-amplitude solutions and in the limit of a rapidly oscillating nonlinear pseudopotential. We show that the presence of the lattice pseudopotential may result in: (i) creation of new LM families which have no counterparts in the case of the uniform nonlinearity; (ii) stabilization of some previously unstable LM species; (iii) evolution of unstable LMs into a pulsating mode trapped in one well of the lattice pseudopotential.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2018.06.019