Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with spatially modulated nonlinearity

Jie Fang Zhang, Yi Shen Li, Jianping Meng, Lei Wu, Boris A. Malomed

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.

Original languageEnglish
Article number033614
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume82
Issue number3
DOIs
StatePublished - 21 Sep 2010

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