Bäcklund transformation, nonlinear superposition formula and solutions of the Calogero equation

In this Letter, the Bäcklund transformation for the (2+1)(2+1)-Calogero equation is presented in the bilinear form. Furthermore, a nonlinear superposition formula related to the transformation is proved rigorously. By the way, the Wronskian determinant solution is also derived and verified completely.