About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

First Page Preview
Ibragimov, Nail H.
Sophus Lie a harmonie v matematické fyzice (k 150. výročí narození). (Czech) [Sophus Lie and harmony in mathematical physics, on the 150th anniversary of his birth]. Pokroky matematiky, fyziky a astronomie, vol. 39 (1994), issue 4, pp. 192-208
MSC: 01A55, 01A60, 17B81, 22-03, 22E70, 35A30, 35Q72 | MR 1309410 | Zbl 0830.01013
Note: Z The Mathematical Intelligencer 16 (1994), č. 1, 20-28. přeložil a upravil O. Kowalski.
Note: From The Mathematical Intelligencer 16 (1994), No. 1, 20-28. translated and annotated O. Kowalski.
References:
[1] Ames, W. F.: Nonlinear Partial Differential Equations in Engineering. Vols. I and II. New York: Academic Press (1965, 1972). MR 0210342 | Zbl 0176.39701
[2] Anderson, R. L., Ibragimov, N. H.: Lie–Bäcklund Transformations in Applications. Philadelphia: SIAM (1979). MR 0520395 | Zbl 0447.58001
[3] Berest, Yu.: Construction of fundamental solutions for Huygens equations as invariant solutions. Dokl. Akad. Nauk SSSR, 317 (4), 786–789 (1991). MR 1121582 | Zbl 0789.35093
[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 0041.53903
[6] Bluman, G. W., Kumei, S.: Symmetries and Differential Equations. New York: Springer-Verlag (1989). MR 1006433 | Zbl 0698.35001
[7] Hawkins, T.: Jacobi and the birth of Lie’s theory of groups. Arch. History Exact Sciences 42 (3), 187–278 (1991). MR 1124967 | Zbl 0767.01019
[8] Hille, E.: Functional Analysis and Semigroups. New York: Amer. Math. Soc. (1948), preface. MR 0025077
[9] Ibragimov, N. H.: Transformation groups Applied to Mathematical Physics. Dordrecht: D. Reidel (1985). MR 0785566 | Zbl 0558.53040
[10] Ibragimov, N. H.: Primer on the Group Analysis. Moscow: Znanie (1989). MR 1063482
[11] Ibragimov, N. H.: Essays in the Group Analysis of Ordinary Differential Equations. Moscow: Znanie (1991). MR 1125762
[12] Ibragimov, N. H.: Group analysis of ordinary differential equations and new observations in mathematical physics. Uspechi Mat. Nauk, to appear. MR 1279026
[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 2348319
[23] Olver, P. J.: Applications of Lie groups to Differential Equations. New York: Springer-Verlag (1986). MR 0836734 | Zbl 0588.22001
[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 0668703
[26] Petrov, A. Z.: Einstein Spaces. Oxford: Pergamon Press (1969). MR 0244912 | Zbl 0174.28305
[27] Polischuk, E. M.: Sophus Lie. Leningrad: Nauka (1983). MR 0742142
[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 0836342 | Zbl 0558.01020
[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 0108122
[32] Stephani, H.: Differential Equations: Their Solution Using Symmetries. Cambridge: Cambridge University Press (1989). MR 1041800 | Zbl 0704.34001
Partner of
EuDML logo