ANALYTICAL SOLUTIONS FOR THE VARIATIONAL EQUATIONS DERIVED FOR THE NONLINEAR SCHRÖDINGER EQUATION: DISPERSION-MANAGED FIBER SYSTEM

Abstract

We consider the nonlinear Schrödinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse, we derive the variational equations. For a particular case of DM fiber systems when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses, we show through numerical simulations that the analytically calculated energy (for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.