On completeness of the Ribaucour transformations for triply orthogonal curvilinear coordinate systems in R3
Abstract
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 R3 (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.
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