  In this paper we solve positively the problem of (local) density of solutions
of the (2+1)-dimentional integrable system describing triply orthogonal
curvilinear coordinates in R^3 (a (2+1)-dimensional generalization of the
3-wave system) obtainable from a given initial solution with consecutive
B\"acklund transformations (called Ribaucour transformations in classical
differential geometry) in the space of all solutions of the system in question.
