Elliptic solutions of the Kadomtsev--Petviashvili equation and integrable systems of particles
Funkcionalʹnyj analiz i ego priloženiâ, Tome 14 (1980) no. 4, pp. 45-54.

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

@article{FAA_1980_14_4_a5,
     author = {I. M. Krichever},
     title = {Elliptic solutions of the {Kadomtsev--Petviashvili} equation and integrable systems of particles},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {45--54},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_1980_14_4_a5/}
}
TY  - JOUR
AU  - I. M. Krichever
TI  - Elliptic solutions of the Kadomtsev--Petviashvili equation and integrable systems of particles
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 1980
SP  - 45
EP  - 54
VL  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_1980_14_4_a5/
LA  - ru
ID  - FAA_1980_14_4_a5
ER  - 
%0 Journal Article
%A I. M. Krichever
%T Elliptic solutions of the Kadomtsev--Petviashvili equation and integrable systems of particles
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 1980
%P 45-54
%V 14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_1980_14_4_a5/
%G ru
%F FAA_1980_14_4_a5
I. M. Krichever. Elliptic solutions of the Kadomtsev--Petviashvili equation and integrable systems of particles. Funkcionalʹnyj analiz i ego priloženiâ, Tome 14 (1980) no. 4, pp. 45-54. http://geodesic.mathdoc.fr/item/FAA_1980_14_4_a5/

[1] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii. Ellipticheskie i avtomorfnye funktsii. Funktsii Lame i Mate, Nauka, M., 1967 | MR

[2] Calogero F., “Exactly solvable one-dimensional many-body systems”, Lett. Nuovo Gimento, 13 (1975), 411–415 | DOI | MR

[3] Perelomov A.M., “Completaly integrable classical systems connected with semisimple Lie algebras”, Lett. Math. Phys., 1 (1977), 531–540 | DOI | MR

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

[5] Krichever I.M., “O ratsionalnykh resheniyakh uravneniya Kadomtseva–Petviashvili i integriruemykh sistemakh $N$ chastits na pryamoi”, Funkts. analiz, 12:1 (1978), 76–78 | MR | Zbl

[6] Choodnovsky D.V., Choodnovsky G.V., “Pole expansions of nonlinear partial differential equations”, Nuovo Cimento B, 40 (1977), 339–350 | DOI | MR

[7] Calogero F., Integrable many-body problem, preprint Univ. di Roma No 89, 1978 | MR

[8] Case K.M., “The $N$-soliton solutions of the Bendgamine-Ono equation”, Proc. Nat. Acad. Sci. USA, 75 (1978), 3562–3563 | DOI | MR | Zbl

[9] Olshanetsky M.A., Perelomov A. M., “Explicite solutions of some completaly integrable systems”, Lett. Nuovo Cimento, 17 (1976), 97–103 | DOI | MR

[10] Olshanetsky M.A., Rogov N.V., “Bound states in completaly integrable systems with two tipes of particles”, Ann. Inst. H. Poincaré, 29 (1978), 169–177 | MR | Zbl

[11] Choodnovsky D.V., “Meromorphic solutions of nonlinear partial differential equations and particle integrable systems”, J. Math. Phys., 20:12 (1979), 2416–2424 | DOI | MR

[12] Dryuma V.C., “Ob analiticheskom reshenii dvumernogo uravneniya Kortevega–de Friza”, Pisma v ZhETF, 19:12 (1973), 219–225

[13] Zakharov V.E., Shabat A.V., “Skhema integrirovaniya nelineinykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi teorii rasseyaniya. I”, Funkts. analiz, 8:3 (1974), 43–53 | MR | Zbl

[14] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1976 | MR

[15] Krichever I.M., “Algebro-geometricheskoe postroenie uravnenii Zakharova–Shabata i ikh periodicheskikh reshenii”, DAN SSSR, 227:2 (1976), 291–294 | MR | Zbl

[16] Krichever I.M., “Integrirovanie nelineinykh uravnenii metodami algebraicheskoi geometrii”, Funkts. analiz, 11:1 (1977), 15–31 | MR | Zbl

[17] Baker H., “Note of foregoing paper «Commutative ordinary differential equation»”, Proc. Royal Soc. London, ser. A, 118 (1928), 570–576 | DOI

[18] Dubpovin B.A., Novikov S.P., “Periodicheskii i uslovno periodicheskii analogi mnogosolitonnykh reshenii uravneniya Kortevega–de Friza”, ZhETF, 67:12 (1974), 2131–2143