Geodesic
Hyperbolic equations with third-order symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 51-67 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We present a complete list of nonlinear one-field hyperbolic equations with integrable third-order $x$ and $y$ symmetries. The list includes both equations of the sine-Gordon type and equations linearizable by differential substitutions.
Keywords: higher symmetry
Mots-clés : sine-Gordon type equation, Liouville-type equation. 
@article{TMF_2011_166_1_a3,
     author = {A. G. Meshkov and V. V. Sokolov},
     title = {Hyperbolic equations with third-order symmetries},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {51--67},
     year = {2011},
     volume = {166},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a3/}
}
TY  - JOUR
AU  - A. G. Meshkov
AU  - V. V. Sokolov
TI  - Hyperbolic equations with third-order symmetries
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 51
EP  - 67
VL  - 166
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a3/
LA  - ru
ID  - TMF_2011_166_1_a3
ER  - 
%0 Journal Article
%A A. G. Meshkov
%A V. V. Sokolov
%T Hyperbolic equations with third-order symmetries
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 51-67
%V 166
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a3/
%G ru
%F TMF_2011_166_1_a3
A. G. Meshkov; V. V. Sokolov. Hyperbolic equations with third-order symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 51-67. http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a3/

[1] V. V. Sokolov, A. B. Shabat, “Classification of integrable evolution equations”, Mathematical Physics Reviews, v. 4, Sov. Sci. Rev., Sect. C, 4, ed. S. P. Novikov, Harwood Academic, Chur, 1984, 221–280 | MR | Zbl

[2] A. V. Mikhailov, A. B. Shabat, R. I. Yamilov, UMN, 42:4(256) (1987), 3–53 | DOI | MR | Zbl

[3] A. V. Mikhailov, A. B. Shabat, V. V. Sokolov, “Simmetriinyi podkhod k klassifikatsii integriruemykh uravnenii”, Integriruemost i kineticheskie uravneniya dlya solitonov, eds. V. G. Bakhtaryar, V. E. Zakharov, V. M. Chernousenko, Naukova dumka, Kiev, 1990, 213–279 | MR | MR | Zbl

[4] S. I. Svinolupov, V. V. Sokolov, Funkts. analiz i ego pril., 16:4 (1982), 86–87 | DOI | MR | Zbl

[5] S. I. Svinolupov, V. V. Sokolov, “O zakonakh sokhraneniya dlya uravnenii, obladayuschikh netrivialnoi algebroi Li–Beklunda”, Integriruemye sistemy, ed. A. B. Shabat, BF AN SSSR, Ufa, 1982, 53–67 | Zbl

[6] A. V. Zhiber, A. B. Shabat, Dokl. AN SSSR, 247:5 (1979), 1103–1107 | MR

[7] A. V. Zhiber, A. B. Shabat, Dokl. AN SSSR, 277:1 (1984), 29–33 | MR | Zbl

[8] A. V. Zhiber, V. V. Sokolov, UMN, 56:1(337) (2001), 63–106 | DOI | MR | Zbl

[9] S. Ya. Startsev, TMF, 120:2 (1999), 237–247 | DOI | MR | Zbl

[10] A. B. Borisov, S. A. Zykov, TMF, 115:2 (1998), 199–214 | DOI | MR | Zbl

[11] J. A. Sanders, J. P. Wang, J. Differ. Equations, 147:2 (1998), 410–434 | DOI | MR | Zbl

[12] A. B. Borisov, S. A. Zykov, M. V. Pavlov, TMF, 131:1 (2002), 126–134 | DOI | MR | Zbl

[13] A. V. Zhiber, Izv. RAN. Ser. matem., 58:4 (1994), 33–54 | DOI | MR | Zbl

[14] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. 3, Ellipticheskie i avtomorfnye funktsii. Funktsii Lame i Mate, Nauka, M., 1967 | MR | MR | Zbl