Application of the theory of catastrophy for studying of мagnetic reconnection
Matematičeskoe modelirovanie, Tome 23 (2011) no. 9, pp. 43-56.

Voir la notice de l'article provenant de la source Math-Net.Ru

The mathematical model of process of magnetic reconnection in a vicinity of critical points is discussed. The diagram method of the catastrophe theory for research of process of transformation of structurally unstable magnetic configurations in structurally stable ones is given. Results of analytical research are confirmed by numerical calculations.
Keywords: magnetic reconnection, catastrophe theory, critical point, diagram method.
Mots-clés : catastrophe germ
@article{MM_2011_23_9_a3,
     author = {D. P. Kostomarov and E. Yu. Echkina and I. N. Inovenkov},
     title = {Application of the theory of catastrophy for studying of {\cyrm}agnetic reconnection},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {43--56},
     publisher = {mathdoc},
     volume = {23},
     number = {9},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_9_a3/}
}
TY  - JOUR
AU  - D. P. Kostomarov
AU  - E. Yu. Echkina
AU  - I. N. Inovenkov
TI  - Application of the theory of catastrophy for studying of мagnetic reconnection
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 43
EP  - 56
VL  - 23
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_9_a3/
LA  - ru
ID  - MM_2011_23_9_a3
ER  - 
%0 Journal Article
%A D. P. Kostomarov
%A E. Yu. Echkina
%A I. N. Inovenkov
%T Application of the theory of catastrophy for studying of мagnetic reconnection
%J Matematičeskoe modelirovanie
%D 2011
%P 43-56
%V 23
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_9_a3/
%G ru
%F MM_2011_23_9_a3
D. P. Kostomarov; E. Yu. Echkina; I. N. Inovenkov. Application of the theory of catastrophy for studying of мagnetic reconnection. Matematičeskoe modelirovanie, Tome 23 (2011) no. 9, pp. 43-56. http://geodesic.mathdoc.fr/item/MM_2011_23_9_a3/

[1] S. I. Syrovatskii, ZhETF, 50 (1966), 1133

[2] V. I. Arnold, Teoriya katastrof, Editorial URSS, M., 2009 | Zbl

[3] B. B. Kadomtsev, “Perezamykanie magnitnykh silovykh linii”, Uspekhi fizicheskikh nauk, 151:1 (1987)

[4] H. P. Furth, J. Killeen, M. N. Rosenbluth, “Finite-Resistivity Instabilities of a Sheet Pinch”, Phys. of Fluids, 6:4 (1963), 459–484 | DOI

[5] K. V. Brushlinskii, A. M. Zaborov, S. I. Syrovatskii, Fizika plazmy, 6:2 (1980), 297

[6] C. V. Bulanov, G. I. Dudnikova, V. P. Zhukov, I. N. Inovenkov, V. V. Pichushkin, Trudy IOFAN, 51 (1996), 101

[7] S. V. Bulanov, E. Yn. Echkina, I. N. Inovenkov, F. Pegoraro, V. V. Pichushkin, “On the structural stability of magnetic configurations with two null lines”, Physics of Plasmas, 6:3 (1999) | DOI | MR

[8] D. P. Kostomarov, S. V. Bulanov, E. Yu. Echkina, I. N. Inovenkov, A. V. Leonenko, V. V. Pichushkin, F. Pegoraro, “Strukturno neustoichivye magnitnye konfiguratsii v trekhmernoi geometrii”, DAN, 390:2 (2003)

[9] D. P. Kostomarov, E. Yu. Echkina, I. N. Inovenkov, S. V. Bulanov, “Modelirovanie magnitnogo perezamykaniya v trekhmernoi geometrii”, Matematicheskoe modelirovanie, 21:11 (2009), 3–15 | MR | Zbl

[10] T. Poston, I. Styuart, Teoriya katastrof i ee prilozheniya, M., 1980

[11] R. Gilmor, Prikladnaya teoriya katastrof, Moskva, M., 1984 | Zbl

[12] T. Breker, L. Lander, Differentsiruemye rostki i katastrofy, Platon, Sankt-Peterburg, 1997

[13] M. Golubitskii, V. Giiemin, Ustoichivye otobrazheniya i ikh osobennosti, Mir, M., 1977 | MR

[14] R. Tom, Strukturnaya ustoichivost i morfogenez, Logos, M., 2002