Dispersion-managed solitons in the limit of large energy

We study a dynamical system for Gaussian dispersion-managed pulses in the limit of large pulse energy and map strength. We show numerically and asymptotically that the pulse energy $E$ grows with the map strength $S$ as $E\sim D_+\sqrt S$, where $D_+$ is the effective dispersion coefficient of the focusing fiber. We also inspect leading-order asymptotic solutions that describe variations of the pulse parameters along the optical fiber.