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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.06432 |
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Table of Contents:
- In this paper, we study the long time behavior of solutions to the defocusing Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS). Using the Gérard-type explicit formula, we prove the scattering result of solutions to this equation with initial data in $L_{+}^{2,α}(\mathbb{R}): = \{u \in L_{+}^2(\mathbb{R}): |x|^α u \in L^2(\mathbb{R})\}$ with some $α>0$. We also characterize the scattering term using the distorted Fourier transform associated with the Lax operator. Following our approach developed in this paper, we can also conclude the asymptotic bound-state/radiation decomposition for global solutions to the focusing (CM-DNLS) with initial data in $L_{+}^{2,α}(\mathbb{R})$ with some $α>0$. This is one of the first works that apply the Gérard-type explicit formula to study the long-time behavior of an integrable equation for a broad class of initial data, beyond the previously studied rational cases.