On dispersion managed nonlinear Schrödinger equations with lumped amplification
Abstract
We show the global well-posedness of the nonlinear Schrödinger equation with periodically varying coefficients and a small parameter $\varepsilon>0$, which is used in optical-fiber communications. We also prove that the solutions converge to the solution for the Gabitov-Turitsyn or averaged equation as $\varepsilon$ tends to zero.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.10381
- arXiv:
- arXiv:2009.10381
- Bibcode:
- 2020arXiv200910381C
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35Q55;
- 35Q60;
- 35A01
- E-Print:
- 17 pages