On the dynamics of dispersion-managed fiber systems with zero Hamiltonian

We consider the nonlinear Schrödinger equation (NLSE), which governs the nonlinear pulse propagation in optical fibers. By means of variational formalism for the NLSE, we derive exact analytical expressions for the variational equations corresponding to the amplitude, width and chirp of the pulse in terms of initial pulse parameters, fiber parameters and the distance of propagation of the pulse; under the condition when the Hamiltonian of the system is zero. Then, for Gaussian and hyperbolic secant ansatz, we check the validity of the obtained analytical results to describe pulse propagation in optical fiber. As a practical application of our results, we consider the design of the dispersion-managed fiber systems and we derive an analytical expression for the Gordon-Haus jitter.