Darboux System as Three-Dimensional Analog of Liouville Equation View Full Text


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Article Info

DATE

2018-12

AUTHORS

R. Ch. Kulaev, A. K. Pogrebkov, A. B. Shabat

ABSTRACT

We discuss the problems of the connections of the modern theory of integrability and the corresponding overdetermined linear systems with works of geometers of the late nineteenth century. One of these questions is the generalization of the theory of Darboux–Laplace transforms for second-order equations with two independent variables to the case of three-dimensional linear hyperbolic equations of the third order. In this paper we construct examples of such transformations. We consider applications to the problem of orthogonal curvilinear coordinate systems in ℝ3. More... »

PAGES

50-58

Journal

TITLE

Russian Mathematics

ISSUE

12

VOLUME

62

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.3103/s1066369x18120046

DOI

http://dx.doi.org/10.3103/s1066369x18120046

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1110658780


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