Theory of connections, Cole--Hopf transformations and potentials of second-order partial differential equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2007), pp. 50-70.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{IVM_2007_9_a2,
     author = {A. K. Rybnikov},
     title = {Theory of connections, {Cole--Hopf} transformations and potentials of second-order partial differential equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {50--70},
     publisher = {mathdoc},
     number = {9},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2007_9_a2/}
}
TY  - JOUR
AU  - A. K. Rybnikov
TI  - Theory of connections, Cole--Hopf transformations and potentials of second-order partial differential equations
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2007
SP  - 50
EP  - 70
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2007_9_a2/
LA  - ru
ID  - IVM_2007_9_a2
ER  - 
%0 Journal Article
%A A. K. Rybnikov
%T Theory of connections, Cole--Hopf transformations and potentials of second-order partial differential equations
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2007
%P 50-70
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2007_9_a2/
%G ru
%F IVM_2007_9_a2
A. K. Rybnikov. Theory of connections, Cole--Hopf transformations and potentials of second-order partial differential equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2007), pp. 50-70. http://geodesic.mathdoc.fr/item/IVM_2007_9_a2/

[1] Bianchi L., “Ricerche sulle superficie a curvatura constante e sulle elicoidi”, Ann. Scuola Norm. Sup. Pisa, 2 (1879), 285 | MR

[2] Lie S., “Zur Theorie der Flächen konstanter Krummung. III; IV”, Arch. Math. Naturvidensk., 5:3 (1880), 282–306; 328–358 | Zbl

[3] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983, 280 pp. | MR

[4] Rogers C., Shadwick W. F., Backlund transformations and their applications, Academic Press, New York–London, 1982 | MR

[5] Backlund A. V., “Zur Theory der partiellen Differentialgleichungen erster Ordnung”, Math. Ann., 17 (1880), 285–328 | DOI | MR

[6] Darboux G., Lecons sur la theorie generale des surfaces, Part 3, Gauthier-Villars, Paris, 1894 | Zbl

[7] Goursat E., Le Probleme de Backlund, Memorial des Sciences Mathematiques. Fasc. VI, Gauthier-Villars, Paris, 1925 | Zbl

[8] Clairin J., “Sur les Transformations de Backlund”, Ann. Sci. Ecole Norm. Sup., 3-e ser., Supple 19, 1902, 1–63 | MR

[9] Pirani F. A. E., Robinson D. C., “Sur la definition des transformations de Backlund”, C.R. Acad. Sc. Paris, Serie A, 285 (1977), 581–583 | MR | Zbl

[10] Pirani F. A. E., Robinson D. C., Shadwick W. F., Local jet-bundle formulation of Backlund transformations, Reidal, Dordrecht (Holland), 1979 | MR | Zbl

[11] Rybnikov A. K., Semenov K. V., “O geometricheskoi interpretatsii otobrazhenii Beklunda”, Invariantnye metody issledovaniya na mnogoobraziyakh struktur geometrii, analiza i matematicheskoi fiziki, Tr. uchastnikov mezhdunarodnoi konferentsii pamyati G. F. Lapteva. Ch. 2 (Moskva, 1999), Izd-vo mekhaniko-matem. f-ta MGU, M., 2001, 172–193

[12] Rybnikov A. K., “Teoriya svyaznostei i preobrazovaniya Beklunda dlya obschikh differentsialnykh uravnenii s chastnymi proizvodnymi vtorogo poryadka”, Dokl. RAN, 405:1 (2005), 26–29 | MR | Zbl

[13] Rybnikov A. K., “O spetsialnykh svyaznostyakh, opredelyayuschikh predstavlenie nulevoi krivizny dlya evolyutsionnykh uravnenii vtorogo poryadka”, Izv. vuzov. Matematika, 1999, no. 9, 32–41 | MR | Zbl

[14] Evtushik L. E., Lumiste Yu. G., Ostianu N. M., Shirokov A. P., “Differentsialno-geometricheskie struktury na mnogoobraziyakh”, Itogi nauki i tekhn. Problemy geometrii, 9, VINITI, M., 1979, 5–246

[15] Laptev G. F., “Differentsialnaya geometriya pogruzhennykh mnogoobrazii. Teoretiko-gruppovoi metod differentsialno-geometricheskikh issledovanii”, Tr. Moskovsk. matem. o-va, no. 2, 1953, 275–382 | MR | Zbl

[16] Laptev G. F., “Teoretiko-gruppovoi metod differentsialno-geometricheskikh issledovanii”, Tr. 3-go Vsesoyuzn. matem. s'ezda, T. 3 (Moskva, 1956), AN SSSR, M., 1958, 409–418

[17] Laptev G. F., “Osnovnye infinitezimalnye struktury vysshikh poryadkov na gladkom mnogoobrazii”, Tr. geometrichesk. seminara, 1, VINITI, M., 1966, 139–189 | MR

[18] Laptev G. F., “Strukturnye uravneniya glavnogo rassloennogo mnogoobraziya”, Tr. geometrichesk. seminara, 2, VINITI, M., 1969, 161–178 | MR

[19] Laptev G. F., “K invariantnoi teorii differentsiruemykh otobrazhenii”, Tr. geometrichesk. seminara, 6, VINITI, M., 1974, 37–42 | MR

[20] Rogers C., Schief W. K., Backlund and Darboux transformations. Geometry and modern applications in soliton theory, Cambridge Univ. Press, 2000 | MR

[21] Ablovits M., Sigur Kh., Solitony i metod obratnoi zadachi, Mir, M., 1987, 480 pp. | MR

[22] Cole J. D., “On a quasilinear parabolic equation occurring in aerodynamics”, Quart. App. Math., 9 (1951), 225–236 | MR | Zbl

[23] Hopf E., “The partial differential equation $u_t+uu_x=\mu u_{xx}$”, Comm. Pure Appl. Math., 1950, 201–230 | DOI | MR | Zbl