Bright solitons in quasi-one dimensional dipolar condensates with spatially modulated interactions

We introduce a model for the condensate of dipolar atoms or molecules, in which the dipole-dipole interaction (DDI) is periodically modulated in space, due to a periodic change of the local orientation of the permanent dipoles, imposed by the corresponding structure of an external field (the necessary field can be created, in particular, by means of magnetic lattices, which are available to the experiment). The system represents a realization of a nonlocal nonlinear lattice, which has a potential to support various spatial modes. By means of numerical methods and variational approximation (VA), we construct bright one-dimensional solitons in this system, and study their stability. In most cases, the VA provides good accuracy, and correctly predicts the stability by means of the Vakhitov-Kolokolov (VK)\ criterion. It is found that the periodic modulation may destroy some solitons, which exist in the usual setting with unmodulated DDI, and can create stable solitons in other cases, not verified in the absence of modulations. Unstable solitons typically transform into persistent localized breathers. The solitons are often mobile, with inelastic collisions between them leading to oscillating localized modes.