Geodesic
On construction of symmetries from integrals of hyperbolic partial differential systems
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 1, pp. 29-37 
D. K. Demskoi; S. Ya. Startsev. On construction of symmetries from integrals of hyperbolic partial differential systems. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 1, pp. 29-37. http://geodesic.mathdoc.fr/item/FPM_2004_10_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An algorithm is proposed which allows one to construct higher symmetries of arbitrary order for some special classes of hyperbolic systems possessing the integrals. The Pohlmeyer–Lund–Regge system and the open two-dimensional Toda lattices are shown to belong to the class of systems such that our algorithm is applicable.

[1] Burbaki N., Gruppy i algebry Li, Mir, M., 1972 | MR | Zbl

[2] Zhiber A. V., “O polnoi integriruemosti dvumernykh dinamicheskikh sistem”, Problemy mekhaniki i upravleniya, Ufimskii nauchnyi tsentr RAN, Ufa, 1994, 62–71

[3] Zhiber A. V., Ibragimov N. Kh., Shabat A. B., “Uravneniya tipa Liuvillya”, DAN SSSR, 249:1 (1979), 26–29 | MR | Zbl

[4] Zhiber A. V., Sokolov V. V., “Preobrazovaniya Laplasa v klassifikatsii integriruemykh kvazilineinykh uravnenii”, Problemy mekhaniki i upravleniya, T. 2, Ufimskii nauchnyi tsentr RAN, Ufa, 1995, 51–65

[5] Zhiber A. V., Sokolov V. V., “Tochno integriruemye uravneniya liuvillevskogo tipa”, Uspekhi mat. nauk, 56:1 (2001), 63–106 | MR | Zbl

[6] Zhiber A. V., Startsev S. Ya., “Integraly, resheniya i suschestvovanie preobrazovanii Laplasa lineinoi giperbolicheskoi sistemy uravnenii”, Mat. zametki, 74:6 (2003), 848–857 | MR | Zbl

[7] Startsev S. Ya., “Ob invariantakh Laplasa sistem giperbolicheskikh uravnenii”, Kompleksnyi analiz, differentsialnye uravneniya, chislennye metody i prilozheniya, T. 3, Institut matematiki s VTs UNTs RAN, Ufa, 1996, 144–154

[8] Trikomi F., Lektsii po uravneniyam v chastnykh proizvodnykh, IL, M., 1957

[9] Shabat A. B., Yamilov R. I., Eksponentsialnye sistemy tipa I i matritsy Kartana, Preprint Bashkirskogo filiala AN SSSR, Ufa, 1981

[10] Anderson I. M., Dutchamp T., “On the existence of global variational principles”, Amer. J. Math., 102 (1980), 781–868 | DOI | MR | Zbl

[11] Darboux G., Leçons sur la théorie générale des surfaces et les applications geometriques du calcul infinitesimal, V. 1–4, Gauthier-Villars, Paris, 1896 | Zbl

[12] Shabat A. B., “Higher symmetries of two-dimensional lattices”, Phys. Lett. A, 200 (1995), 121–133 | DOI | MR | Zbl