Geodesic
Reduction of the self-dual Yang–Mills equations on subgroups of the extended Poincaré group
Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 3, pp. 416-432 Cet article a éte moissonné depuis la source Math-Net.Ru

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We have obtained ansatzes for the vector-potential of the Yang–Mills field in the Minkowski space $R(1,3)$ invariant under 3-parameter subgroups of the extended Poincaré group $\widetilde P(1,3)$. Using these, we carry out symmetry reduction of the self-dual Yang–Mills equations to systems of ordinary differential equations. 
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     title = {Reduction of the self-dual {Yang{\textendash}Mills} equations on subgroups of the extended {Poincar\'e} group},
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V. I. Lahno; W. I. Fushchych. Reduction of the self-dual Yang–Mills equations on subgroups of the extended Poincaré group. Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 3, pp. 416-432. http://geodesic.mathdoc.fr/item/TMF_1997_110_3_a5/

[1] A. Actor, Rev. Mod. Phys., 51:3 (1979), 461 | DOI | MR

[2] M. K. Prasad, “Instantony i monopoli v teoriyakh kalibrovochnykh polei Yanga–Millsa”, Geometricheskie idei v fizike, Mir, M., 1983, 64

[3] S. Chakravarty, M. J. Ablowitz, P. A. Clarcson, Phys. Rev. Lett., 65:9 (1990), 1085 | DOI | MR | Zbl

[4] S. Chakravarty, S. L. Kent, E. T. Newman, J. Math. Phys., 36:2 (1995), 763 | DOI | MR | Zbl

[5] J. Tafel, J. Math. Phys., 34:5 (1993), 1892 | DOI | MR | Zbl

[6] M. Kovalyov, M. Légaré, L. Gagnon, J. Math. Phys., 34:7 (1993), 3245 | DOI | MR | Zbl

[7] T. A. Ivanova, A. D. Popov, Phys. Lett. A, 205 (1995), 158 | DOI | MR | Zbl

[8] M. Legaré, A. D. Popov, Phys. Lett. A, 198 (1995), 195 | DOI | MR | Zbl

[9] F. Schwarz, Lett. Math. Phys., 6:5 (1982), 355 | DOI | MR | Zbl

[10] P. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, 1993 | MR

[11] L. V. Ovsyannikov, Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[12] W. I. Fushchych, W. N. Shtelen, Lett. Nuovo Cim., 38:2 (1983), 37 | DOI | MR

[13] W. Fushchych, W. Shtelen, N. Serov, Symmetry Analysis and Exact Solutions of Equation of Nonlinear Mathematical Physics, Kluwer Academic Publishers, Dordrecht, 1993 | MR | Zbl

[14] V. Lahno, R. Zhdanov, W. Fushchych, J. Nonlinear Math. Physics, 2:1 (1995), 51 | DOI | MR | Zbl

[15] R. Z. Zhdanov, V. I. Lahno, W. I. Fushchych, UMZh, 47:4, 456 | MR | Zbl

[16] R. Z. Zhdanov, W. I. Fushchych, J. Phys. A: Math. Gen., 28 (1995), 6253 | DOI | MR | Zbl

[17] J. Patera, P. Winternitz, H. Zassenhaus, J. Math. Phys, 16:8, 1615 | DOI | MR | Zbl

[18] V. I. Fuschich, L. F. Barannik, A. F. Barannik, Podgruppovoi analiz grupp Galileya, Puankare i reduktsiya nelineinykh uravnenii, Naukova dumka, Kiev, 1991 | MR | Zbl

[19] V. I. Fuschich, R. Z. Zhdanov, Nelineinye spinornye uravneniya: simmetriya i tochnye resheniya, Naukova dumka, Kiev, 1992 | MR | Zbl