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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2502.17968 |
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| _version_ | 1866909509622956032 |
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| author | Chen, Xi |
| author_facet | Chen, Xi |
| contents | We consider the defocusing Calogero--Moser derivative nonlinear Schr{ö}dinger equation\begin{align*}i \partial_{t} u+\partial_{x}^2 u-2ΠD\left(|u|^{2}\right)u=0, \quad (t,x ) \in \mathbb{R} \times \mathbb{R}\end{align*}posed on $E := \left\{u \in L^{\infty}(\mathbb{R}): u' \in L^{2}(\mathbb{R}), u'' \in L^{2}(\mathbb{R}), |u|^{2}-1 \in L^{2}(\mathbb{R})\right\}$. We prove the global well-posedness of this equation in $E$. Moreover, we give an explicit formula for the chiral solution to this equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17968 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The defocusing Calogero--Moser derivative nonlinear Schr{ö}dinger equation with a nonvanishing condition at infinity Chen, Xi Analysis of PDEs We consider the defocusing Calogero--Moser derivative nonlinear Schr{ö}dinger equation\begin{align*}i \partial_{t} u+\partial_{x}^2 u-2ΠD\left(|u|^{2}\right)u=0, \quad (t,x ) \in \mathbb{R} \times \mathbb{R}\end{align*}posed on $E := \left\{u \in L^{\infty}(\mathbb{R}): u' \in L^{2}(\mathbb{R}), u'' \in L^{2}(\mathbb{R}), |u|^{2}-1 \in L^{2}(\mathbb{R})\right\}$. We prove the global well-posedness of this equation in $E$. Moreover, we give an explicit formula for the chiral solution to this equation. |
| title | The defocusing Calogero--Moser derivative nonlinear Schr{ö}dinger equation with a nonvanishing condition at infinity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.17968 |