Stability of matter-wave solitons in optical lattices

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (gamma (1)) is less than that of the LOL (V (0)) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For gamma (1) > V (0), only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for gamma (1) < V (0). We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.