On the rational solutions of Zakharov–Shabat equations and completely integrable systems of $N$ particles on a line

All decreasing rational solutions of the Kadomtzev–Petviashvili equations are constructed. The motion of the poles of a solution is identified with the motion of $N$ particles on the line via Calogero–Moser hamiltonians. This Hamiltonian system is thus included in the theory of algebro-geometric solutions of Zakharov–Shabat equations.