Averaging of dispersion managed nonlinear Schrödinger equations

2021/08/17 by Choi, Mi-Ran, Lee, Young-Ran
#35Q55 #35Q60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.07444

Abstract

We consider the dispersion managed power-law nonlinear Schrödinger(DM NLS) equations with a small parameter ε > 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 H¹(ℝ) as ε goes to zero. Meanwhile, in the positive average dispersion, we obtain the global existence of the solution to DM NLS equation in H¹(ℝ) for sufficiently small ε > 0, even when the exponent of the nonlinearity is beyond the mass-critical power.

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