Regularity of ground state solutions of dispersion managed nonlinear schrödinger equations

We consider the dispersion managed nonlinear Schrödinger equation (DMNLS) in the case of zero residual dispersion. Using dispersive properties of the equation and estimates in Bourgain spaces we show that the ground state solutions of DMNLS are smooth. The existence of smooth solutions in this case matches the well-known smoothness of the solutions in the case of nonzero residual dispersion. In the case x∈R2 we prove that the corresponding minimization problem with zero residual dispersion has no solution.