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

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

1996-06-11

arxiv.org/abs/solv-int/9606002v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

7 pages (26 Kbytes), standard LaTeX 2.09, run twice to get the right cross-references. Resubmitted with the only correction: a

Scientific paper

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.

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