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We study the zero-dispersion limit of the Calogero-Moser derivative NLS equation $$i\partial_tu+\partial_x^2 u \pm2D\Pi(|u|^2)u=0 , \qquad x\in\mathbb{R},$$ starting from an initial data $u_0\in L^2_+(\mathbb{R})\cap L^\...