The Calogero equation and Liouville type equations

In this paper we present a two-component generalization of the C-integrable Calogero equation (see [1]). This system is C-integrable as well, and moreover we show that the Calogero equation and its two-component generalization are solvable by a reciprocal transformation to ODE's. Simultaneously we obtain a generalized Liouville equation (34), determined by two arbitrary functions of one variable.