The defocusing Calogero–Moser derivative nonlinear Schrödinger equation with a nonvanishing condition at infinity
Résumé
We consider the defocusing Calogero–Moser derivative nonlinear Schrödinger equation
\begin{align*}
i \partial_{t} u+\partial_{x}^2 u-2\Pi D\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.
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