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arXiv · 2108.07444

Averaging of dispersion managed nonlinear Schr\"odinger equations

Mi-Ran Choi·Young-Ran Lee
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Abstract

We consider the dispersion managed power-law nonlinear Schr\"odinger(DM NLS) equations with a small parameter $\varepsilon > 0$ 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 $H^1(\mathbb{R})$ as $\varepsilon$ goes to zero. Meanwhile, in the positive average dispersion, we obtain the global existence of the solution to DM NLS equation in $H^1(\mathbb{R})$ for sufficiently small $\varepsilon > 0$, even when the exponent of the nonlinearity is beyond the mass-critical power.

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Mi-Ran Choi, Young-Ran Lee. 2021-08-17. Averaging of dispersion managed nonlinear Schr\"odinger equations. https://arxiv.org/abs/2108.07444

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