Real elliptic solutions of the “sine-Gordon” equation
Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 231-240 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A method is proposed for constructing real finite-zone elliptic solutions of the sine-Gordon equation. Examples are considered of new elliptic smooth solutions of genera 2 and 3.
@article{SM_1991_70_1_a13,
     author = {A. O. Smirnov},
     title = {Real elliptic solutions of the {{\textquotedblleft}sine-Gordon{\textquotedblright}} equation},
     journal = {Sbornik. Mathematics},
     pages = {231--240},
     year = {1991},
     volume = {70},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_70_1_a13/}
}
TY  - JOUR
AU  - A. O. Smirnov
TI  - Real elliptic solutions of the “sine-Gordon” equation
JO  - Sbornik. Mathematics
PY  - 1991
SP  - 231
EP  - 240
VL  - 70
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1991_70_1_a13/
LA  - en
ID  - SM_1991_70_1_a13
ER  - 
%0 Journal Article
%A A. O. Smirnov
%T Real elliptic solutions of the “sine-Gordon” equation
%J Sbornik. Mathematics
%D 1991
%P 231-240
%V 70
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1991_70_1_a13/
%G en
%F SM_1991_70_1_a13
A. O. Smirnov. Real elliptic solutions of the “sine-Gordon” equation. Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 231-240. http://geodesic.mathdoc.fr/item/SM_1991_70_1_a13/

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

[2] Akhiezer N. I., Elementy teorii ellipticheskikh funktsii, Nauka, M., 1970 | MR | Zbl

[3] Belokolos E. D., Bobenko A. I., Matveev V. B., Enolskii V. Z., “Algebro-geometricheskie printsipy superpozitsii konechnozonnykh reshenii integriruemykh nelineinykh uravnenii”, UMN, 41:2 (1986), 3–42 | MR | Zbl

[4] Belokolos E. D., Enolskii V. Z., “Obobschennyi anzats Lemba”, TMF, 53:2 (1982), 271–282 | MR | Zbl

[5] Bobenko A. I., “O periodicheskikh konechnozonnykh resheniyakh uravneniya sine-Gordon”, Funktsion. analiz i ego pril., 18:3 (1984), 73–74 | MR | Zbl

[6] Dodd G., Eilbek Dzh., Gibbon Dzh., Moris Kh., Solitony i nelineinye volnovye uravneniya, Mir, M., 1988 | MR

[7] Dubrovin B. A., Natanzon S. M., “Veschestvennye dvukhzonnye resheniya uravneniya «sine-Gordon»”, Funktsion. analiz i ego pril., 16:1 (1982), 27–43 | MR | Zbl

[8] Dubrovin B. A., Novikov S. P., “Periodicheskii i uslovno periodicheskii analogi mnogosolitonnykh reshenii uravneniya Kortevega - de Friza”, ZhETF, 67:6 (1974), 2131–2143 | MR

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

[10] Kalodzhero F., Degasperis A., Spektralnye preobrazovaniya i solitony, Mir, M., 1985 | MR

[11] Kozel V. A., Kotlyarov V. P., “Pochti-periodicheskie resheniya uravneniya «sine-Gordon»”, DAN USSR, ser. A, 10 (1976), 878–881 | MR

[12] Krichever I. M., “Ellipticheskie resheniya uravneniya Kadomtseva - Petviashvili i integriruemye sistemy chastits”, Funktsion. analiz i ego pril., 14:4 (1980), 45–54 | MR | Zbl

[13] Smirnov A. O., “Matrichnyi analog teoremy Appelya i reduktsii mnogomernykh teta-funktsii Rimana”, Matem. sb., 133(175) (1987), 382–391 | Zbl

[14] Smirnov A. O., “Konechnozonnye resheniya abelevoi tsepochki Toda roda 4 i 5 v ellipticheskikh funktsiyakh”, TMF, 78:1 (1989), 11–21 | MR

[15] Springer Dzh., Vvedenie v teoriyu rimanovykh poverkhnostei, IL, M., 1960

[16] Takhtadzhyan L. A., Faddeev L. D., Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[17] Airault H., McKean H., Moser J., “Rational and elliptic solutions of the $\mathrm{KdV}$ equation and related many-body problem”, Comm. on Pure and Appl. Math., 30 (1977), 95–125 | DOI | MR

[18] Belokolos E. D., Enol'skii V. Z., Verdier potentials and Weierstrass reduction theory, Preprint of the Institute of Metall, Physics, Kiev, 1988, No1 | MR | Zbl

[19] Costabile G., Parmetier R. D., Savo B., McLaughlin D. W., Scott A. C., “Exact solutions of the “sine-Gordon” equation describing oscillations in a long (but finite) Josephson junction”, Appl. Phys. Lett., 32 (1978), 587–589 | DOI

[20] Matveev V. B., Abelian functions and solitons, Preprint No373, Univ. of Wroclaw, 1976, 13 pp.

[21] Verdier J.-L., New elliptic solitons, Preprint, 1988, 13 pp. | MR