On completeness of the Ribaucour transformations for triply orthogonal curvilinear coordinate systems in R^3

E. I. Ganzha

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On completeness of the Ribaucour transformations for triply orthogonal curvilinear coordinate systems in R^3

E. I. Ganzha

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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 R^3 (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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E. I. Ganzha. 1997-01-20. On completeness of the Ribaucour transformations for triply orthogonal curvilinear coordinate systems in R^3. https://arxiv.org/abs/solv-int/9606002

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