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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.00119 |
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Table of Contents:
- We study the zero-dispersion limit of the Calogero-Moser derivative NLS equation $$i\partial_tu+\partial_x^2 u \pm\,2DΠ(|u|^2)u=0, \qquad x\in\mathbb{R},$$ starting from an initial data $u_0\in L^2_+(\mathbb{R})\cap L^\infty (\mathbb{R}),$ where $D=-i\partial_x,$ and $Π$ is the Szegő projector defined as $\widehat{Πu}(ξ)=1_{[0,+\infty)}(ξ)\widehat{u}(ξ).$ We characterize the zero-dispersion limit solution by an explicit formula. Moreover, we identify it, in terms of the branches of the multivalued solution of the inviscid Burgers-Hopf equation. Finally, we infer that it satisfies a maximum principle.