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We introduce a model for the condensate of dipolar atoms or molecules, inwhich 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 necessaryfield can be created, in particular, by means of magnetic lattices, which areavailable to the experiment). The system represents a realization of a nonlocalnonlinear lattice, which has a potential to support various spatial modes. Bymeans of numerical methods and variational approximation (VA), we constructbright one-dimensional solitons in this system, and study their stability. Inmost cases, the VA provides good accuracy, and correctly predicts the stabilityby means of the Vakhitov-Kolokolov (VK)\ criterion. It is found that theperiodic modulation may destroy some solitons, which exist in the usual settingwith unmodulated DDI, and can create stable solitons in other cases, notverified in the absence of modulations. Unstable solitons typically transforminto persistent localized breathers. The solitons are often mobile, withinelastic collisions between them leading to oscillating localized modes.

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