On completeness of the Ribaucour transformations for triply orthogonal curvilinear coordinate systems in R3
E. I. Ganzha
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 Bäcklund transformations (called Ribaucour transformations in classical differential geometry) in the space of all solutions of the system in question.
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