On a class of elliptic potentials of the Dirac operator

We show that there exists a class of finite-gap potentials of the Dirac operator and finite-gap solutions of the 'decomposed' non-linear Schrödinger equation which are single-valued meromorphic functions of $x$. It is also shown that the evolution of the poles $x_j(t)$ of these elliptic solutions satisfies the dynamics of the Calogero–Moser system