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arXiv · 2511.06432

Scattering of the defocusing Calogero--Moser derivative nonlinear Schr\"odinger equation

Xi Chen
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Abstract

In this paper, we study the long time behavior of solutions to the defocusing Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS). Using the G\'erard-type explicit formula, we prove the scattering result of solutions to this equation with initial data in $L_{+}^2(\mathbb{R}):=\left\{f \in L^2(\mathbb{R}): \operatorname{supp}(\widehat{f}) \subset[0,+\infty)\right\}$. We also characterize the scattering term using the distorted Fourier transform associated with the Lax operator. This is one of the first works that apply the G\'erard-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.

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Xi Chen. 2025-11-09. Scattering of the defocusing Calogero--Moser derivative nonlinear Schr\"odinger equation. https://arxiv.org/abs/2511.06432

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