@article{TMF_2000_122_1_a11,
author = {S. P. Tsarev},
title = {Factoring linear partial differential operators and the {Darboux} method for integrating nonlinear partial differential equations},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {144--160},
year = {2000},
volume = {122},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a11/}
}
TY - JOUR AU - S. P. Tsarev TI - Factoring linear partial differential operators and the Darboux method for integrating nonlinear partial differential equations JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2000 SP - 144 EP - 160 VL - 122 IS - 1 UR - http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a11/ LA - ru ID - TMF_2000_122_1_a11 ER -
%0 Journal Article %A S. P. Tsarev %T Factoring linear partial differential operators and the Darboux method for integrating nonlinear partial differential equations %J Teoretičeskaâ i matematičeskaâ fizika %D 2000 %P 144-160 %V 122 %N 1 %U http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a11/ %G ru %F TMF_2000_122_1_a11
S. P. Tsarev. Factoring linear partial differential operators and the Darboux method for integrating nonlinear partial differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 144-160. http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a11/
[1] G. Darboux, Ann. Ecole Normale Sup., VII (1870), 163–173 | DOI | MR
[2] I. M. Anderson, N. Kamran, Duke Math. J., 87:2 (1997), 265–319 | DOI | MR | Zbl
[3] M. Juras, “Generalized Laplace invariants and classical integration methods for second order scalar hyperbolic partial differential equations in the plane”, Proc. of the 6th Int. Conf. (Brno, Czech Republik, Aug. 28–Sept. 1, 1995), ed. J. Janyska, Masaryk University Press, Brno, 1996, 275–284 | MR | Zbl
[4] A. V. Zhiber, V. V. Sokolov, S. Ya. Startsev, Dokl. RAN, 343:6 (1995), 746–748 | MR | Zbl
[5] G. Darboux, Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal, V. 1–4, Gautier-Villar, Paris, 1887–1896 | MR
[6] E. Landau, J. Reine Angew. Math., 124 (1901/1902), 115–120 | MR | Zbl
[7] S. P. Tsarev, “An algorithm for complete enumeration of all factorizations of a linear ordinary differential operator”, Proc. of the 1996 Int. Symp. on Symbolic and Algebraic Computation (ISSAC'96) (Zuerich, Switzerland, July 24–26, 1996), ed. Y. N. Lakshman, ACM Press, New York, 1996, 226–231 | DOI | Zbl
[8] A. Loewy, Math. Ann., 56 (1903), 549–584 | DOI | MR | Zbl
[9] A. Loewy, Math. Ann., 62 (1906), 89–117 | DOI | MR | Zbl
[10] O. Ore, Ann. Math., 34 (1933), 480–508 | DOI | MR | Zbl
[11] E. Beke, Math. Ann., 45 (1894), 278–300 | DOI | MR
[12] H. Blumberg, Über algebraische Eigenschaften von linearen homogenen Differentialausdrücken, Diss., Univ. Göttingen, Göttingen, 1912
[13] K. Aierlend, M. Rouzen, Klassicheskoe vvedenie v sovremennuyu teoriyu chisel, Mir, M., 1987 | MR
[14] O. Ore, Ann. Math., 32 (1931), 463–477 | DOI | MR | Zbl
[15] G. Birkgof, Teoriya reshetok, Mir, M., 1984 | MR
[16] G. Grätzer, General lattice theory, Akademie-Verlag, Berlin, 1978 | MR | Zbl
[17] N. Jacobson, Lectures in abstract algebra. V. 1. Basic Concepts, D. Van Nostrand Co., Inc., Toronto–New York–London, 1951 | MR
[18] E. Goursat, Am. J. Math., 18 (1896), 347–385 | DOI | MR | Zbl