Existence of dispersion management solitons for general nonlinearities

We give a proof of existence of solitary solutions of the dispersion management equation for positive and zero average dispersion for a large class of nonlinearities. These solutions are found as minimizers of nonlinear and nonlocal variational problems which are invariant under a large non compact group. Our proof of existence of minimizers is rather direct and avoids the use of Lions' concentration compactness argument. The existence of dispersion managed solitons is shown under very mild conditions on the dispersion profile and the nonlinear polarization of optical active medium, which cover all physically relevant cases for the dispersion profile and a large class of nonlinear polarizations.