Geodesic
On Bäcklund correspondences
Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 277-293 
V. V. Zharinov. On Bäcklund correspondences. Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 277-293. http://geodesic.mathdoc.fr/item/SM_1989_64_1_a16/
@article{SM_1989_64_1_a16,
     author = {V. V. Zharinov},
     title = {On {B\"acklund} correspondences},
     journal = {Sbornik. Mathematics},
     pages = {277--293},
     year = {1989},
     volume = {64},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_64_1_a16/}
}
TY  - JOUR
AU  - V. V. Zharinov
TI  - On Bäcklund correspondences
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 277
EP  - 293
VL  - 64
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1989_64_1_a16/
LA  - en
ID  - SM_1989_64_1_a16
ER  - 
%0 Journal Article
%A V. V. Zharinov
%T On Bäcklund correspondences
%J Sbornik. Mathematics
%D 1989
%P 277-293
%V 64
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1989_64_1_a16/
%G en
%F SM_1989_64_1_a16

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

In the framework of a geometric approach to nonlinear systems of partial differential equations, a Bäcklund correspondence is defined according to a representation of it as a differential connection between two such systems, and a construction of it is presented. Examples of the practical realization of this construction are given. Bibliography: 7 titles.

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

[2] Backlund Transformations, Lect. Notes Math., 515, ed. R. M. Miura, Springer, Heidelberg, 1976 | MR | Zbl

[3] Vinogradov A. M., Krasilschik I. S, Lychagin V. V., Vvedenie v geometriyu nelineinykh differentsialnykh uravnenii, Nauka, M., 1986 | MR

[4] Tsujishita T., “On variation bicomplexes associated to differential equations”, Osaka J. Math., 19 (1982), 311–363 | MR | Zbl

[5] Wells R. O., Jr., “Complex manifolds and mathematical physics”, Bull. Amer. Math. Soc., 1, 1979, 2, 293–336 ; Uells R. O., “Kompleksnye mnogoobraziya i matematicheskaya fizika”, Tvistory i kalibrovachnye polya, Mir, M., 1983, 163–171 | MR

[6] Zharinov V. V., “Zakony sokhraneniya evolyutsionnykh sistem”, TMF, 68:2 (1986), 163–171 | MR | Zbl

[7] Zharinov V. V., “Formula Grina dlya nelineinykh sistem uravnenii v chastnykh proizvodnykh”, DAN SSSR, 296:4 (1987), 785–787 | MR