Exponential Decay of Dispersion-Managed Solitons for General Dispersion Profiles

We show that any weak solution of the dispersion management equation describing dispersion-managed solitons together with its Fourier transform decay exponentially. This strong regularity result extends a recent result of Erdo?an, Hundertmark, and Lee in two directions, to arbitrary non-negative average dispersion and, more importantly, to rather general dispersion profiles, which cover most, if not all, physically relevant cases.