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arXiv · 2605.30657

Well-posedness for the periodic Intermediate nonlinear Schr\"{o}dinger equation

Andreia Chapouto·Justin Forlano·Thierry Laurens
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Abstract

We study the well-posedness for the intermediate nonlinear Schr\"{o}dinger equation (INLS) with periodic boundary conditions. Using a gauge transform, we obtain large data local well-posedness in $H^{s}(\mathbb{T})$ for any $s\geq \frac 12$. We extend this result to global well-posedness under a small $L^2$-norm constraint by exploiting the complete integrability of the continuum Calogero-Moser equation (CCM). We also establish additional results such as the unconditional well-posedness in the energy space and the convergence of solutions to INLS to those of CCM in the infinite-depth limit.

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Andreia Chapouto, Justin Forlano, Thierry Laurens. 2026-05-28. Well-posedness for the periodic Intermediate nonlinear Schr\"{o}dinger equation. https://arxiv.org/abs/2605.30657

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