J. Belmonte-Beitia and D. Pelinovsky

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

Applicable Analysis 89, 1335-1350 (2010)

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.

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