PreprintarXiv licencearXiv
On Analyticity of Solitons for the Periodic Dispersion-Managed Nonlinear Schrödinger Equation
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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BibTeX
@misc{herr2026analyticity,
title = {{On Analyticity of Solitons for the Periodic Dispersion-Managed Nonlinear Schrödinger Equation}},
author = {Sebastian Herr and Dirk Hundertmark and Jeremy L. Marzuola and Tim Van Hoose},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07535},
eprint = {2609.07535},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07535},
}
RIS
TY - UNPB
TI - On Analyticity of Solitons for the Periodic Dispersion-Managed Nonlinear Schrödinger Equation
AU - Sebastian Herr
AU - Dirk Hundertmark
AU - Jeremy L. Marzuola
AU - Tim Van Hoose
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07535
UR - https://arxiv.org/abs/2609.07535
AB - 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.
ER -