2018/02/28 by G. L. Alfimov, L. A. Gegel, M. E. Lebedev +2 · 1 citation
Physics and Astronomy · #cond-mat.quant-gas #nlin.PS
paper · pdf · doi:10.1016/j.cnsns.2018.06.019
published as Commun Nonlinear Sci Numer Simulat 66 (2019) 194-207 · to be published in Commun. Nonlin. Sci. Numer. Simul
arxiv created 2018/06/18 · arxiv updated 2018/07/11
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 on 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.