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Bäcklund’s theorem for submanifolds of space forms and a generalized wave equation. (English) Zbl 0618.53017

On reprend les résultats de l’auteur et C. L. Terng [Ann. Math., II. Ser. 111, 477-490 (1980; Zbl 0462.35079)] et C. L. Terng [ibid. 4, 491-510 (1980; Zbl 0447.53001)] obtenus par le théorème de Bäcklund généralisé et on montre que l’interprétation analytique vérifie une transformation de Bäcklund et une formule de superposition pour des systèmes d’équations à dérivées partielles généralisant les équations des ondes homogènes ainsi que l’équation de Sine-Gordon.
Reviewer: V.Obadeanu

MSC:

53B25 Local submanifolds
53B20 Local Riemannian geometry
35L05 Wave equation
35Q99 Partial differential equations of mathematical physics and other areas of application
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References:

[1] Ablowitz, M. J., Beals, R.; Tenenblat, K.On the solution of the generalized wave and generalized Sine-Gordon Equations. (to appear). · Zbl 0646.35058
[2] Bianchi, L.,Sopra le deformazioni isogonali delle superficie a curvatura constante in geometria ellittica ed iperbolica. Annali di Matem. (3)18 (1911) 185–243. · JFM 42.0642.02 · doi:10.1007/BF02420539
[3] Cartan, E.,Sur les variētēs de courbure constante d’un space euclidien ou non-euclidien. Bull. Soc. Math. France47 (1919) 125–160 and48 (1920), 132–208. · JFM 47.0692.03 · doi:10.24033/bsmf.997
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[5] Tenenblat, K., and Terng, C. L.Bäcklund’s theorem for n-dimensional submanifolds of R 2n , Annals of Math,111 (1980), 477–490. · Zbl 0462.35079 · doi:10.2307/1971105
[6] Terng, C.L.A higher dimension generalization of the Sine-Gordon equation and its soliton theory, Annals of Math, (1980), 491–510. · Zbl 0447.53001
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