Geodesic
New exact solutions of the Born–Infeld model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 24, Tome 465 (2017), pp. 135-146 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Lagrangian and Hamiltonian of the Born–Infeld model in the cartesian as well in the light cone variables are given. Using the auto-Backlund transformation the new solutions of the corresponding nonlinear equation are constructed. In particular, the “dressed” Barbashov–Chernikov's solution is obtained. 
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E. Sh. Gutshabash; P. P. Kulish. New exact solutions of the Born–Infeld model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 24, Tome 465 (2017), pp. 135-146. http://geodesic.mathdoc.fr/item/ZNSL_2017_465_a7/

[1] M. Born, L. Infeld, Proc. R. Soc. Lond. A, 144 (1934), 425 | DOI | Zbl

[2] D. D. Ivanenko, A. A. Sokolov, Klassicheskaya teoriya polya, GITTL, M., 1951

[3] S. V. Ketov, PIERS Proceedings, Moscow, 2009, 110 pp.

[4] G. Felder, L. Kofman, A. Starobinsky, JHEP, 0209 (2002), 026 ; arXiv: hep-th/0208019 | DOI

[5] L. Bers, Matematicheskie voprosy dozvukovoi i okolozvukovoi gazovoi dinamiki, IL., M., 1961 | MR

[6] E. Sh. Gutshabash, Pisma v ZhETF, 99:12 (2014), 827 ; arXiv: 1409.6741 | DOI

[7] L. A. Takhtadzhan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR

[8] M. Arik, F. Neyzi, Y. Nutku, P. Olver, J. M. Verosky, IMA Preprint Series, 497, 1989

[9] O. F. Menshikh, Mat. zametki, 77:4 (2005), 551 | DOI | MR | Zbl

[10] K. Mallory, R. A. van Gorder, K. Vajravelu, Comm. Nonlin. Sci. Num. Simul., 19 (2014), 1669–1674 | DOI | MR

[11] V. I. Fuschich, V. M. Shtelen, N. I. Serov, Simmetriinyi analiz i tochnye resheniya nelineinykh uravnenii matematicheskoi fiziki, Naukova dumka, Kiev, 1989 ; M. Nadjafikhah, S. R. Hejazi, arXiv: 1009.5490 | MR

[12] B. M. Barbashov, N. A. Chernikov, ZhETF, 50 (1996), 1296–1308

[13] Dzh. Uizem, Lineinye i nelineinye volny, Nauka, M., 1974

[14] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady, v. 1, Fizmatlit, M., 2002 | MR

[15] J. Brunelli, M. Gürses, K. Zheltukhin, Rev. Math. Phys., 13 (2001), 529 | MR | Zbl

[16] E. Sh. Gutshabash, Zap. nauchn. semin. POMI, 374, 2010, 121–135 | Zbl

[17] F. Kalodzhero, Integriruemost i kineticheskie uravneniya dlya solitonov, Naukova dumka, Kiev, 1990, 65–116 | MR