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arXiv · 2609.07535

On Analyticity of Solitons for the Periodic Dispersion-Managed Nonlinear Schr\"odinger Equation

Sebastian Herr·Dirk Hundertmark·Jeremy L. Marzuola·Tim Van Hoose
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Abstract

We explore the regularity of energy maximizers for the Lagrangian of a periodic dispersion managed fiber optic at fixed intensity, on a torus of length $L$ and with vanishing average dispersion. We show that the Fourier coefficients decay at a polynomial rate, and then upgrade this to exponential decay, so that the maximizers are analytic in space for large enough $L$. In addition, by an asymptotic comparison to the optimizers on the real line, we prove that the solutions are non-trivial. We also consider a conjecture that the maximizer necessarily has an underlying symmetry inherent to both the energy functional and the resulting Euler-Lagrange equation. All of our results are supported with illustrative numerical experiments.

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Sebastian Herr, Dirk Hundertmark, Jeremy L. Marzuola, Tim Van Hoose. 2026-09-07. On Analyticity of Solitons for the Periodic Dispersion-Managed Nonlinear Schr\"odinger Equation. https://arxiv.org/abs/2609.07535

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