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J. Belmonte-Beitia and D. Pelinovsky

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

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Applicable Analysis 89, 1335-1350 (2010)

**Abstract:**

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 et al. [PRE 77, 016604 (2008)]
and Smerzi & Trombettoni [PRA 68, 023613 (2003)], we show that
the intersite cubic nonlinear terms in the discrete nonlinear Schrodinger (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.

**Keywords:**

Gross-Pitaevskii equation, existence of gap solitons, discrete nonlinear Schrodinger equation,
justification of amplitude equations, semiclassical limit