Geodesic
About integrals of linear nonautonomous multidimensional differential systems which are integrated in closed form
Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 65-71.

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

Three classes of completely solvable linear nonautonomous multidimensional differential systems (diagonalizable systems, triangular systems, the Lappo–Danilevsky systems) are considered. The regular methods of building first integrals for these differential systems are developed. In addition, some examples are given to illustrate the obtained results.
Keywords: system of total differential equations, first integral. 
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A. F. Pranevich; P. B. Pauliuchyk. About integrals of linear nonautonomous multidimensional differential systems which are integrated in closed form. Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 65-71. http://geodesic.mathdoc.fr/item/PFMT_2015_2_a10/

[1] G. Darboux, “Mémoire sur les équations differentielles algebriques du premier ordre et du premier degré”, Bulletin des Sciences Mathématiques, 2 (1878), 60–96 ; 123–144 ; 151–200 | Zbl

[2] V. V. Amelkin, Avtonomnye i lineinye mnogomernye differentsialnye uravneniya, Editorial URSS, M., 2003, 144 pp.

[3] I. V. Gaishun, Vpolne razreshimye mnogomernye differentsialnye uravneniya, Editorial URSS, M., 2004, 272 pp. | MR

[4] V. N. Gorbuzov, A. F. Pronevich, “Spektpalnyi metod postpoeniya integpalnogo bazisa yakobievoi sistemy v chastnykh ppoizvodnykh”, Differents. uravneniya i protsessy upravleniya, 2001, no. 3, 17–45 | MR

[5] V. N. Gorbuzov, A. F. Pronevich, “Postroenie integralov lineinoi differentsialnoi sistemy”, Vesnik Grodzenskaga dzyarzhaunaga un-ta. Ser. 2, 2003, no. 2(22), 50–60

[6] V. N. Gorbuzov, A. F. Pronevich, “Integraly $R$-lineinykh sistem v polnykh differentsialakh”, Doklady NAN Belarusi, 48:1 (2004), 49–52 | MR | Zbl

[7] V. N. Gorbuzov, A. F. Pronevich, “Postroenie pervykh integralov lineinykh nestatsionarnykh mnogomernykh differentsialnykh sistem prostoi matrichnoi struktury”, Vestnik BGU. Ser. 1, 2008, no. 2, 75–79 | MR | Zbl

[8] A. F. Pronevich, R-differentsiruemye integraly sistem v polnykh differentsialakh, LAP LAMBERT Academic Publishing, Saarbruchen, 2011, 104 pp.

[9] V. N. Gorbuzov, A. F. Pranevich 1201.4141v1 [math.DS], First integrals of ordinary linear differential systems, Cornell Univ., Ithaca, New York, 2012, 75 pp., arXiv: \href{http://arxiv.org/abs/alg-geom/9511010}

[10] V. V. Kozlov, Simmetrii, topologiya i rezonansy v gamiltonovoi mekhanike, Izd-vo Udmurtskogo un-ta, Izhevsk, 1995, 432 pp. | MR

[11] V. N. Gorbuzov, Integraly differentsialnykh sistem, GrGU, Grodno, 2006, 447 pp.

[12] A. Goriely, Integrability and nonintegrability of dynamical systems, Advanced series on nonlinear dynamics, 19, World Scientific, 2001, 436 pp. | MR | Zbl

[13] R. Khorn, Ch. Dzhonson, Matrichnyi analiz, Mir, M., 1989, 655 pp. | MR

[14] I. A. Lappo-Danilevskii, Primenenie funktsii ot matrits k teorii lineinykh sistem obyknovennykh differentsialnykh uravnenii, Gostekhizdat, M., 1957, 456 pp. | MR

[15] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1966, 576 pp. | MR