Averaging of dispersion managed nonlinear Schrodinger equations

초록

We consider the dispersion managed power-law nonlinear Schrodinger (DM NLS) equations with a small parameter epsilon > 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 epsilon 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 epsilon > 0, even when the exponent of the nonlinearity is beyond the mass-critical power.

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