Geodesic
Multidimensional nonlinear systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 3, pp. 411-419 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of the construction and of the integrability of systems of nonlinear partial differential equations in a multidimensional space is discussed. A proposed algebraic-geometric construction is illustrated for the example of completely integrable equations of the Bourlet type and their generalizations, for which, in particular, Bäcklund transformations are obtained. 
@article{TMF_1986_69_3_a8,
     author = {M. V. Saveliev},
     title = {Multidimensional nonlinear systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {411--419},
     year = {1986},
     volume = {69},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_69_3_a8/}
}
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M. V. Saveliev. Multidimensional nonlinear systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 3, pp. 411-419. http://geodesic.mathdoc.fr/item/TMF_1986_69_3_a8/

[1] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov: Metod obratnoi zadachi, Nauka, M., 1980 | MR

[2] Bullaf R., Kodri F. (red.), Solitony, Mir, M., 1983

[3] Leznov A. N., Savelev M. V., Gruppovye metody integrirovaniya nelineinykh dinamicheskikh sistem, Nauka, M., 1985 | MR | Zbl

[4] Jimbo M., Miwa T., Publ. RIMS, Kyoto Univ., 19 (1983), 943–1001 | DOI | MR | Zbl

[5] Leznov A. N., Manko V. I., Chumakov S. M., Trudy FIAN, 167, Nauka, M., 1985

[6] Zakharov V. E., Manakov S. V., Funkts. analiz i ego prilozh., 19 (1985), 11–25 | MR

[7] Savelev M. V., TMF, 60:1 (1984), 9–23 | MR | Zbl

[8] Bitt J. F., Differential algebra, Amer. Math. Coll. Publ., 33, N. Y., 1950 ; Kolchin E. R., Differential algebra and algebraic groups, Acad. Press, N. Y., 1973 | MR | MR | Zbl

[9] Kac V. G., Infinite dimensional Lie algebras, Birkhauser, Boston, 1983 | MR | Zbl

[10] Bianchi L., Lezioni di geometria differenziale, V. 2, part 2, N. Zanichelli, Bologna, 1924 | Zbl

[11] Eizenkhart L. P., Rimanova geometriya, IL, M., 1948

[12] Aminov Yu. A., Matem. sb., 111(153):3 (1980), 402–433 | MR | Zbl

[13] Tenenblat K., Chuu-Lian Terng, Ann. Math., 111 (1980), 477–490 | DOI | MR | Zbl

[14] Savelev M. V., Mnogomernye nelineinye dinamicheskie sistemy. I: Predstavlenie tipa nulevoi krivizny, Preprint IFVE 85-130, IFVE, Serpukhov, 1985 | MR