Group analysis methods for construction and investigation of the bifurcation equation

B. V. Loginov

Applications of Mathematics (1992)

  • Volume: 37, Issue: 4, page 241-248
  • ISSN: 0862-7940

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Loginov, B. V.. "Group analysis methods for construction and investigation of the bifurcation equation." Applications of Mathematics 37.4 (1992): 241-248. <http://eudml.org/doc/15712>.

@article{Loginov1992,
author = {Loginov, B. V.},
journal = {Applications of Mathematics},
keywords = {symmetry group; crystallographic groups; bifurcation equation; symmetry group; crystallographic groups; bifurcation equation},
language = {eng},
number = {4},
pages = {241-248},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Group analysis methods for construction and investigation of the bifurcation equation},
url = {http://eudml.org/doc/15712},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Loginov, B. V.
TI - Group analysis methods for construction and investigation of the bifurcation equation
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 4
SP - 241
EP - 248
LA - eng
KW - symmetry group; crystallographic groups; bifurcation equation; symmetry group; crystallographic groups; bifurcation equation
UR - http://eudml.org/doc/15712
ER -

References

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  1. B. V. Loginov, Branching theory of solutions of nonlinear equations in conditions of group invariance, FAN, Tashkent, 1985. (In Russian.) (1985) MR0878356
  2. B. V. Loginov V. A. Trenogin, On the use of group invariance in bifurcation theory, Differential Equations 11 no. 8 (1975), 1518-1521. (In Russian.) (1975) MR0380541
  3. J. Dieudonne J. Carrel D. Mamfold, Geometric theory of invariants, Mir, Moskva, 1974. (1974) 
  4. L. V. Ovsjannikov, Group analysis of differential equations, Nauka, Moskva, 1978, (In Russian.) (1978) MR0511921
  5. L. V. Ovsjanikov, Lectures on the theory of group properties of differential equations, NGU, Novosibirsk, 1966. (In Russian.) (1966) 
  6. N. Ch. Ibragimov, Groups of transformations in mathematical physics, Nauka, Moskva, 1983. (In Russian.) (1983) 
  7. B. V. Loginov, Ch. R. Rachmatova N. Juldashev, On construction of bifurcation equation by its symmetry group, (cristallographic groups), Mixed type equations and free boundary value problems, FAN, Tashkent, 1985, pp. 183-195. (In Russian.) (1985) 
  8. B. V. Loginov A. O. Kusnetsov, On construction of periodic solutions of three-dimensional problem of capillary-gravitational waves over a flat bottom in the case of high degeneracy, Proc. ICNO-11, Budapest, Aug. 17-23, 1987, Budapest, 1987, pp. 669-671. (In Russian.) (1987) 
  9. B. V. Loginov S. G. Sabirova, On the bifurcation of periodic solutions of nonlinearly perturbed elliptic equations, Izvestija AN Uzbek SSR, fiz.-mat, nauki no. 4 (1988), 32-37. (In Russian.) (1988) MR0979383
  10. M. M. Vainberg V. A. Trenogin, Branching theory of solutions of nonlinear equations, Nauka, Moskva, 1969 (In Russian.); in English transl., Naardorf, Leyden, 1974. (1969) 
  11. Ch. Kittel, Introduction into solid states physics, Nauka, Moskva, 1978. (In Russian.) (1978) 
  12. W. Heine, Group theory in quantum mechanics, IL, Moskva, 1969. (In Russian.) (1969) 
  13. G. Ja. Ljubarsky, Group theory and its applications in physics, GITTL, Moskva, 1958. (1958) 
  14. Ph. Delanō, 10.1007/BF01168578, Manuscripta mathematica no. 1 (1983), 29-45. (1983) MR0722920DOI10.1007/BF01168578
  15. T. Aubin, Metriques Riemanniennes et Courbure, J. Diff. Geometry 48(1970), 383-424. (1970) Zbl0212.54102MR0279731
  16. I. M. Vinogradov, Foundations of the number theory, Nauka, Moskva, 1981. (1981) 

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