| Title:
|
Group analysis methods for construction and investigation of the bifurcation equation (English) |
| Author:
|
Loginov, B. V. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
241-248 |
| . |
| Category:
|
math |
| . |
| Keyword:
|
symmetry group |
| Keyword:
|
crystallographic groups |
| Keyword:
|
bifurcation equation |
| MSC:
|
20H15 |
| MSC:
|
37C80 |
| MSC:
|
37G99 |
| MSC:
|
47H15 |
| MSC:
|
58E09 |
| idZBL:
|
Zbl 0795.58035 |
| idMR:
|
MR1180602 |
| DOI:
|
10.21136/AM.1992.104506 |
| . |
| Date available:
|
2008-05-20T18:43:42Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104506 |
| . |
| Reference:
|
[1] B. V. Loginov: Branching theory of solutions of nonlinear equations in conditions of group invariance.FAN, Tashkent, 1985. (In Russian.) MR 0878356 |
| Reference:
|
[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.) MR 0380541 |
| Reference:
|
[3] J. Dieudonne J. Carrel D. Mamfold: Geometric theory of invariants.Mir, Moskva, 1974. |
| Reference:
|
[4] L. V. Ovsjannikov: Group analysis of differential equations.Nauka, Moskva, 1978, (In Russian.) MR 0511921 |
| Reference:
|
[5] L. V. Ovsjanikov: Lectures on the theory of group properties of differential equations.NGU, Novosibirsk, 1966. (In Russian.) |
| Reference:
|
[6] N. Ch. Ibragimov: Groups of transformations in mathematical physics.Nauka, Moskva, 1983. (In Russian.) |
| Reference:
|
[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.) |
| Reference:
|
[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.) |
| Reference:
|
[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.) MR 0979383 |
| Reference:
|
[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. |
| Reference:
|
[11] Ch. Kittel: Introduction into solid states physics.Nauka, Moskva, 1978. (In Russian.) |
| Reference:
|
[12] W. Heine: Group theory in quantum mechanics.IL, Moskva, 1969. (In Russian.) |
| Reference:
|
[13] G. Ja. Ljubarsky: Group theory and its applications in physics.GITTL, Moskva, 1958. |
| Reference:
|
[14] Ph. Delanō: Bifurcation for Monge-Ampere equations on flat tori.Manuscripta mathematica no. 1 (1983), 29-45. MR 0722920, 10.1007/BF01168578 |
| Reference:
|
[15] T. Aubin: Metriques Riemanniennes et Courbure.J. Diff. Geometry 48(1970), 383-424. Zbl 0212.54102, MR 0279731 |
| Reference:
|
[16] I. M. Vinogradov: Foundations of the number theory.Nauka, Moskva, 1981. |
| . |
