Modulation instability in a medium with a nonlocal nonlinearity

The general conditions of appearance of the modulation instability of spatially homogeneous regimes in media with a nonlocal response of nonlinearity are determined. By using, as an example, the nonlocality in the form of the truncated Lennard-Jones potential, which is characteristic of interatomic interaction in Bose-Einstein condensates, the region of stability is found and the character of structures arising upon the loss of stability is discussed.