Averaged model and integrable limits in nonlinear double-periodic Hamiltonian systems

We derive average propagation model for a nonlinear wave dynamics in media with periodically varying parameters considering a general case with differ ent periods of the nonlinearity and dispersion oscillations. Applying quasi -identical canonical transformation we find the conditions when the average d Hamiltonian dynamics is close to an integrable model. We apply general th eory to the practical problem of optical signal transmission in fiber lines with short-scale dispersion management.