Averaging of dispersion managed nonlinear Schrödinger equations

Abstract

Abstract We consider the dispersion managed power-law nonlinear Schrödinger (DM NLS) equations with a small parameter ɛ > 0 and the averaged equation, which are used in optical fiber communications. We prove that the solutions of DM NLS equations converge to the solution of the averaged equation in H 1 ( R ) as ɛ goes to zero. Meanwhile, in the positive average dispersion, we obtain the global existence of the solution to DM NLS equation in H 1 ( R ) for sufficiently small ɛ > 0, even when the exponent of the nonlinearity is beyond the mass-critical power.