Investigation of stability of optical solitons propagation in dispersion managed transmission systems

This report is devoted to a stability investigation of pair solitons propagation in transmission DM lines using Lyapunov analysis based on a classical stability criterions of evolution of dynamical systems in different field in nonlinear physics. The evolution of the optical signal envelope along the cascaded fiber transmission system is given by nonlinear Schrodinger equation (NLSE). The results show that dynamic systems with minimum energy losses display general tendency, which leads to the instability of impulse propagation On the other hand, the dynamic systems, that has an energy dissipation, are more stable due to external perturbations. However this criteria is a relative one, it is necessary to achieve a sequence of solutions for some range of parameters of solitons impulses to give the decision concerning a stability of an impulse propagation along the solitons line.