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A fundamental property of Monge characteristics in involutive systems of non-linear partial differential equations and its application

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References

  1. Bourbaki, N.: Éléments de mathématique. algèbre commutative. Chap. IV. Paris: Hermann 1961

    Google Scholar 

  2. Cartan, E.: Sur l'intégration des systèmes d'équations aux différentielles totales. Ann. Sci. Éc. Norm. Super., 3e Sér.18, 241–311 (1901)

    Google Scholar 

  3. Cartan, E.: Les systèmes de Pfaff à cinq variables et les équations aux dérivées partielles du second ordre. Ann. Sci. Éc. Norm. Super.27, 109–192 (1910)

    Google Scholar 

  4. Cartan, E.: Sur les systèmes en involution d'équations aux dérivées partielles du second ordre à une fonction inconnue de trois variables indépendentes. Bull. Soc. Math. Fr.39, 352–443 (1911)

    Google Scholar 

  5. Cartan, E.: Les systèmes différentiels extérieurs et leurs applications géométriques. Paris: Hermann 1945

    Google Scholar 

  6. Cinquini-Cibrario, M.: Un teorema di esistenza e di unicità per un sistema di equazioni alle derivate parziali. Ann. Mat. Pura Appl. (4)24, 157–175 (1945)

    Google Scholar 

  7. Forsyth, A.R.: Theory of differential equations. Part IV, Vol. VI. London: Cambrige University Press 1906

    Google Scholar 

  8. Friedrichs, K.O., Lewy, H.: Das Anfangswertproblem einer beliebigen nicht-linearen hyperbolischen Differentialgleichungen beliebiger Ordnung in zwei Variablen. Existenz, Eindeutgkeit und Abhängigkeitsbereich der Lösung. Math. Ann.99, 200–221 (1928)

    Google Scholar 

  9. Goldschmidt, H.: Integrability criteria for systems of non-linear partial differential equations. J. Differ. Geom.1, 269–307 (1967)

    Google Scholar 

  10. Goursat, E.: Leçon sur l'intégration des équations aux dérivées partielles du second ordre à deux variables indépendentes. Tom. II. Paris: Hermann 1898

    Google Scholar 

  11. Goursat, E.: Leçon sur le problème de Pfaff. Paris: Hermann 1922

    Google Scholar 

  12. Goursat, E.: Le problème de Bäcklund. Mem. Sci. Mat. no 6. Paris: Gauthier-Villars 1925

    Google Scholar 

  13. Hermann, R.: Geometric theory of non-linear differential equations, Bäcklund transformations and solitons. Part B Interdisciplinary Mathematics Vol. 14, Brookline: Math. Sci. Press 1977

    Google Scholar 

  14. Kähler, E.: Einführung in die Theorie der Systeme von Differentialgleichungen. Leipzig: Teubner 1934

    Google Scholar 

  15. Kakié, K.: On involutive systems of partial differential equations in two independent variables. J. Fac. Sci. Univ. Tokyo, Sect. IA21, 405–433 (1974)

    Google Scholar 

  16. Kakié, K.: Algebraic structures of characteristics in involutive systems of non-linear partial differential equations. Publ. RIMS Kyoto Univ.13, 107–158 (1977)

    Google Scholar 

  17. Kuranishi, M.: On E. Cartan's prolongation theorem of exterior differential systems. Am. J. Math.79, 1–47 (1957)

    Google Scholar 

  18. Kuranishi, M.: Lectures on involutive systems of partial differential equations São Paulo: Pub. Soc. Mat. 1967

    Google Scholar 

  19. Matsuda, M.: Cartan-Kuranishi's prolongation of differential systems combined with that of Lagrange and Jacobi. Publ. RIMS Kyoto Univ.3, 69–84 (1967)

    Google Scholar 

  20. Matsuda, M.: Generalized Pfaff's problem. J. Fac. Sci. Univ. Tokyo, Sect. IA19, 231–242 (1972)

    Google Scholar 

  21. Pommaret, J.F.: Systems of partial differential equations and Lie pseudogroups. New York: Gordon and Breach 1978

    Google Scholar 

  22. Serre, J.-P.: Algèbre locale, multiplicités. Lect. Notes Math., 11. Berlin, Heidelberg, New York: Springer 1965

    Google Scholar 

  23. Yang, D.: Involutive hyperbolic differential systems. Thesis, Harvard Univ., Cambridge, 1983

    Google Scholar 

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  1. Department of Mathematics, Rikkyo University, Nishi-Ikebukuro, 171, Tokyo, Japan

    Kunio Kakié

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  1. Kunio Kakié
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Kakié, K. A fundamental property of Monge characteristics in involutive systems of non-linear partial differential equations and its application. Math. Ann. 273, 89–114 (1985). https://doi.org/10.1007/BF01455916

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