Elliptic solutions of nonlinear equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 84 (1990) no. 1, pp. 38-45 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A method is described for constructing algebraic curves whose theta functions reduce to one-dimensional functions. This makes it possible to construct finite-gap solutions of nonlinear equations expressed in terms of the elliptic functions. Elliptic two-gap potentials of the Schrödinger operator different from the Lamé and Verdier potentials are constructed.
@article{TMF_1990_84_1_a3,
     author = {I. A. Taimanov},
     title = {Elliptic solutions of~nonlinear equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {38--45},
     year = {1990},
     volume = {84},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_84_1_a3/}
}
TY  - JOUR
AU  - I. A. Taimanov
TI  - Elliptic solutions of nonlinear equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1990
SP  - 38
EP  - 45
VL  - 84
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1990_84_1_a3/
LA  - ru
ID  - TMF_1990_84_1_a3
ER  - 
%0 Journal Article
%A I. A. Taimanov
%T Elliptic solutions of nonlinear equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1990
%P 38-45
%V 84
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1990_84_1_a3/
%G ru
%F TMF_1990_84_1_a3
I. A. Taimanov. Elliptic solutions of nonlinear equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 84 (1990) no. 1, pp. 38-45. http://geodesic.mathdoc.fr/item/TMF_1990_84_1_a3/

[1] Dubrovin B. A., Matveev V. B., Novikov S. P., UMN, 31:1 (1976), 55–136 | MR | Zbl

[2] Dubrovin B. A., Krichever I. M., Novikov S. P., Sovremennye problemy matematiki. Fundamentalnye napravleniya, 4, VINITI, M., 1985, 179–285 | MR | Zbl

[3] Belokolos E. D., Bobenko A. I., Matveev V. B., Enolskii V. Z., UMN, 41:2 (1986), 3–42 | MR | Zbl

[4] Dubrovin B. A., Novikov S. P., ZhETF, 67:12 (1974), 2131–2143 | MR

[5] Krichever I. M., Funkts. analiz i ego prilozh., 14:4 (1980), 45–54 | MR | Zbl

[6] Verdier J.-L., New elliptic solitons, Preprint, Paris, 1987 | MR

[7] Fay J. D., Lect. Notes in Math., 352, Springer, 1973 | DOI | MR | Zbl

[8] Dalalyan S. G., UMN, 29:6 (1974), 165–166 | MR | Zbl

[9] Dalalyan S. G., Matem. sb., 98:2 (1975), 255–267 | MR | Zbl

[10] Taimanov I. A., Geometricheskie aspekty nekotorykh nelineinykh sistem, Dis. ...kand. fiz.-mat. nauk, MGU, M., 1987

[11] Belokolos E. D., Enolskii V. Z., Funkts. analiz i ego prilozh., 23:1 (1989), 57–58 | MR | Zbl

[12] Babich M. V., Bobenko A. I., Matveev V. B., Izv. AN SSSR, ser. matem., 49:3 (1985), 511–529 | MR | Zbl

[13] Smirnov A. O., TMF, 78:1 (1989), 11–21 | MR

[14] Dubrovin B. A., Natanzon S. M., Funkts. analiz i ego prilozh., 16:1 (1982), 27–43 | MR | Zbl

[15] Belokolos E. D., Enolskii V. Z., TMF, 53:2 (1982), 271–282 | MR | Zbl

[16] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. 3, Nauka, M., 1967 | MR

[17] Dubrovin B. A., UMN, 36:2 (1981), 11–80 | MR | Zbl