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The extension of Darboux’s method to systems in involution of partial differential equations of arbitrary order in two independent variables. (English) Zbl 0302.35029


MSC:

35G20 Nonlinear higher-order PDEs
35A25 Other special methods applied to PDEs
58A10 Differential forms in global analysis
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[1] E. Cartan: Sur integration des systemes d’equations aux differentielles totales. Ann. Sci. Ecole Norm. Sup., 3e serie, 18, 241-311 (1901). · JFM 32.0351.04
[2] E. Cartan: Sur la structure des groupes infinis de transformations. Ann. Sci. Ecole Norm. Sup., 3e serie, 21, 153-206 (1904). · JFM 35.0176.04
[3] E. Cartan: Les systemes de Pfaff a cinq variables et les equations aux derivees partielles du second ordre. Ann. Sci. Ecole Norm. Sup., 3e serie, 27, 109- 192 (1910). · JFM 41.0417.01
[4] E. Cartan: Lemons sur les invariants integraux. Hermann, Paris (1922). · Zbl 0212.12501
[5] E. Cartan: Les systemes differentiels exterieurs et leurs application geometriques. Hermann, Paris (1945). · Zbl 0063.00734
[6] G. Cerf: Sur les transformations des equations aux derivees partielles d’ordre quelconque a deux variables independentes. J. de Math., 7e serie, 4, 309-412 (1918). · JFM 46.0716.04
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[8] E. Goursat: Lemons sur Pintegration des equations aux derivees partielles du second ordre a deux variables independentes, Tom. II. Hermann, Paris (1898). · JFM 29.0310.01
[9] E. Goursat: Legons sur le probleme de Pfaff. Hermann, Paris (1922). · JFM 48.0538.01
[10] Y. Matsushima: On a theorem concerning the prolongation of a differential system. Nagoya Math. J., 6, 1-16 (1953). · Zbl 0052.31905
[11] I. G. Petrovskii: Lectures on Partial Differential Equations (2nd ed.). Gos. Izd. Tekh.-Teor. Lit., Moscow (1953).
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