Bifurcation of gap solitons in periodic potentials with a sign-varying nonlinearity coefficient

Details Bifurcation of gap solitons in periodic potentials with a sign-varying nonlinearity coefficient Bifurcation of gap solitons in periodic potentials with a sign-varying nonlinearity coefficient

2009-06-13

arxiv.org/abs/0906.2501v1

Nonlinear Sciences

Pattern Formation and Solitons

18 pages, 2 figures, submitted to Applicable Analysis

Scientific paper

We address the Gross--Pitaevskii (GP) equation with a periodic linear potential and a periodic sign-varying nonlinearity coefficient. Contrary to the claims in the previous works of Abdullaev {\em et al.} [PRE {\bf 77}, 016604 (2008)] and Smerzi & Trombettoni [PRA {\bf 68}, 023613 (2003)], we show that the intersite cubic nonlinear terms in the discrete nonlinear Schr\"odinger (DNLS) equation appear beyond the applicability of assumptions of the tight-binding approximation. Instead of these terms, for an even linear potential and an odd nonlinearity coefficient, the DNLS equation and other reduced equations for the semi-infinite gap have the quintic nonlinear term, which correctly describes bifurcation of gap solitons.

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