On one family of finite gap curvilinear orthogonal coordinates
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 947-954.

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We propose a generalization of the procedure for constructing curvilinear orthogonal coordinates and, in particular, show how the isothermal elliptic coordinates on the plane are derived in the framework of the generalized construction.
Keywords: curvilinear orthogonal coordinates, elliptic coordinates.
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O. A. Bogoyavlenskaya. On one family of finite gap curvilinear orthogonal coordinates. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 947-954. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a48/

[1] G. Darboux, Lecons sur le Systemés Ortogonaux et Coordonnées Curvilignes, Gauthier–Villars, Paris, 1910 | Zbl

[2] V. E. Zakharov, “Description of the $n$-orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type. I: Integration of the Lamé equation”, Duke Math. J., 94:1 (1998), 103–139 | DOI | MR | Zbl

[3] I. M. Krichever, “Algebraic-geometric n-orthogonal curvilinear coordinate systems and solutions of the associativity equations”, Functional Analysis and Its Applications, 31:1 (1997), 32–50 | DOI | MR | Zbl

[4] A. E. Mironov, I. A. Taimanov, “Orthogonal curvilinear coordinate systems corresponding to singular spectral curves”, Proceedings of the Steklov Institute of Mathematics, 255, 2006, 180–196 | DOI | MR | Zbl

[5] I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Mathematical Surveys, 66:1 (2011), 111–150 | DOI | MR | Zbl