A nonlinear Schr\"odinger equation (NLS) with dispersion averaged
nonlinearity of saturated type is considered. Such a nonlocal NLS is of
integro-differential type and it arises naturally in modeling fiber-optics
communication systems with periodically varying dispersion profile (dispersion
management). The associated constrained variational principle is shown to
posses a ground state solution by constructing a convergent minimizing sequence
through the application of a method similar to the classical concentration
compactness principle of Lions. One of the obstacles in applying this
variational approach is that a saturated nonlocal nonlinearity does not satisfy
uniformly the so-called strict sub-additivity condition. This is overcome by
applying a special version of Ekeland's variational principle.Comment: 24 page
