@article{PMFA_1994_39_4_a2,
author = {Ibragimov, Nail H.},
title = {Sophus {Lie} a harmonie v matematick\'e fyzice (k 150. v\'yro\v{c}{\'\i} narozen{\'\i})},
journal = {Pokroky matematiky, fyziky a astronomie},
pages = {192--208},
year = {1994},
volume = {39},
number = {4},
mrnumber = {1309410},
zbl = {0830.01013},
language = {cs},
url = {http://geodesic.mathdoc.fr/item/PMFA_1994_39_4_a2/}
}
Ibragimov, Nail H. Sophus Lie a harmonie v matematické fyzice (k 150. výročí narození). Pokroky matematiky, fyziky a astronomie, Tome 39 (1994) no. 4, pp. 192-208. http://geodesic.mathdoc.fr/item/PMFA_1994_39_4_a2/
[1] Ames, W. F.: Nonlinear Partial Differential Equations in Engineering. Vols. I and II. New York: Academic Press (1965, 1972). | MR | Zbl
[2] Anderson, R. L., Ibragimov, N. H.: Lie–Bäcklund Transformations in Applications. Philadelphia: SIAM (1979). | MR | Zbl
[3] Berest, Yu.: Construction of fundamental solutions for Huygens equations as invariant solutions. Dokl. Akad. Nauk SSSR, 317 (4), 786–789 (1991). | MR | Zbl
[4] Bianchi, L.: Lezioni sulla teoria dei gruppi continui finiti di transformazioni. Pisa: Spoerri (1918).
[5] Birkhoff, G.: Hydrodynamics. Princeton, NJ: Princeton University Press (1950, 1960). | Zbl
[6] Bluman, G. W., Kumei, S.: Symmetries and Differential Equations. New York: Springer-Verlag (1989). | MR | Zbl
[7] Hawkins, T.: Jacobi and the birth of Lie’s theory of groups. Arch. History Exact Sciences 42 (3), 187–278 (1991). | MR | Zbl
[8] Hille, E.: Functional Analysis and Semigroups. New York: Amer. Math. Soc. (1948), preface. | MR
[9] Ibragimov, N. H.: Transformation groups Applied to Mathematical Physics. Dordrecht: D. Reidel (1985). | MR | Zbl
[10] Ibragimov, N. H.: Primer on the Group Analysis. Moscow: Znanie (1989). | MR
[11] Ibragimov, N. H.: Essays in the Group Analysis of Ordinary Differential Equations. Moscow: Znanie (1991). | MR
[12] Ibragimov, N. H.: Group analysis of ordinary differential equations and new observations in mathematical physics. Uspechi Mat. Nauk, to appear. | MR
[13] Klein, F.: Theorie der Transformationsgruppen B. III, Pervoe prisuzhdenie premii N. I. Lobachevskogo, 22 okt. 1897 goda. Kazan: Tipo-litografiya Imperatorskogo Universiteta (1898), pp. 10–28.
[14] Laplace, P. S.: Mécanique céleste. T. I. Livre 2, Chap. III (1799).
[15] Lie, S.: Über die Integration durch bestimmte Integrale von einer Klasse linearer partieller Differentialgleichungen. Arch. for. Math. VI (1881).
[16] Lie, S.: Klassifikation und Integration von gewöhnlichen Differentialgleichungen zwischen $x$, $y$, die eine Gruppe von Transformationen gestatten. Arch. Math. VIII, 187–453 (1883).
[17] Lie, S.: Theorie der Transformationsgruppen, Bd. 1. (Bearbeitet unter Mitwirkung von F. Engel). Leipzig: B. G. Teubner (1888).
[18] Lie, S.: Die infinitesimalen Berührungstransformationen der Mechanik. Leipz. Ber. (1889).
[19] Lie, S.: Vorlesungen über Differentialgleichungen mit bekannten infinitesimalen Transformationen (Bearbeitet und herausgegeben von Dr. G. Scheffers). Leipzig: B. G. Teubner (1891).
[20] Lie, S.: Zur allgemeinen Theorie der partiellen Differentialgleichungen beliebiger Ordnung. Leipz. Ber. I, 53–128 (1895).
[21] Lie, S.: Gesammelte Abhandlungen, Bd. 1–6. Leipzig–Oslo.
[22] Noether, M.: Sophus Lie. Math. Annalen 53, 1–4 (1990). | MR
[23] Olver, P. J.: Applications of Lie groups to Differential Equations. New York: Springer-Verlag (1986). | MR | Zbl
[24] Ovsjanikov, L. V.: Group properties of differential equations. Novosibirsk: USSR Academy of Science, Siberian Branch (1962).
[25] Ovsjanikov, L. V.: Group Analysis of Differential Equations. Boston: Academic Press (1982). | MR
[26] Petrov, A. Z.: Einstein Spaces. Oxford: Pergamon Press (1969). | MR | Zbl
[27] Polischuk, E. M.: Sophus Lie. Leningrad: Nauka (1983). | MR
[28] Puknachev, V. V.: Invariant solutions of Navier–Stokes equations describing free-boundary motions. Dokl. Akad. Nauk SSSR 20 (2), 302–305 (1972).
[29] Purkert, W.: Zum Verhältnis von Sophus Lie und Friedrich Engel. Wiss. Zeitschr. Ernst-Moritz-Arndt-Universität Greifswald, Math.-Naturwiss. Reihe XXXIII, Heft 1–2, 29–34 (1984). | MR | Zbl
[30] Riemann, G. F. B.: Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite. Abh. K. Ges. Wiss. Göttingen 8 (1860).
[31] Sedov, L. I.: Similarity and Dimensional Methods in Mechanics, 4th ed. New York: Academic Press (1959). | MR
[32] Stephani, H.: Differential Equations: Their Solution Using Symmetries. Cambridge: Cambridge University Press (1989). | MR | Zbl