On equation of minimal surface in $\mathbb R^3$: different representations, properties of exact solutions, conservation laws
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 21, Tome 374 (2010), pp. 121-135 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Various representations of the equation of minimal surface in $\mathbb R^3$ are considered. Properties of exact solutions are studied and a procedure to construct the corresponding conservation laws is suggested. Links between the solutions of this equation and those of the elliptic version of the Monge–Ampere equation are found. Bibl. – 19 titles.
@article{ZNSL_2010_374_a7,
     author = {E. Sh. Gutshabash},
     title = {On equation of minimal surface in~$\mathbb R^3$: different representations, properties of exact solutions, conservation laws},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--135},
     year = {2010},
     volume = {374},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a7/}
}
TY  - JOUR
AU  - E. Sh. Gutshabash
TI  - On equation of minimal surface in $\mathbb R^3$: different representations, properties of exact solutions, conservation laws
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2010
SP  - 121
EP  - 135
VL  - 374
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a7/
LA  - ru
ID  - ZNSL_2010_374_a7
ER  - 
%0 Journal Article
%A E. Sh. Gutshabash
%T On equation of minimal surface in $\mathbb R^3$: different representations, properties of exact solutions, conservation laws
%J Zapiski Nauchnykh Seminarov POMI
%D 2010
%P 121-135
%V 374
%U http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a7/
%G ru
%F ZNSL_2010_374_a7
E. Sh. Gutshabash. On equation of minimal surface in $\mathbb R^3$: different representations, properties of exact solutions, conservation laws. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 21, Tome 374 (2010), pp. 121-135. http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a7/

[1] A. V. Pogorelov, Differentsialnaya geometriya, Nauka, M., 1969 | MR

[2] B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, Sovremennaya geometriya, Nauka, M., 1986 | MR | Zbl

[3] Dao Chong Tkhi, A. T. Fomenko, Minimalnye poverkhnosti i problema Plato, Nauka, M., 1991 | MR

[4] S. N. Bernshtein, Sobr. soch., v. 3, Izd-vo AN SSSR, M., 1960

[5] P. Osserman, UMN, 22:4 (1967), 55 | MR | Zbl

[6] Minimalnye poverkhnosti, Fizmatlit, M., 2003

[7] A. B. Borisov, DAN, 389:5 (2003), 603 | MR | Zbl

[8] A. Moro, 2009, arXiv: 0808.1235v3[physics.optics]

[9] V. Blyashke, Vvedenie v differentsialnuyu geometriyu, Regulyarnaya i khaoticheskaya dinamika, M.–Izhevsk, 2007

[10] A. D. Polyanin, V. F. Zaitsev, A. I. Zhurov, Metody resheniya nelineinykh uravnenii matematicheskoi fiziki i mekhaniki, Fizmatlit, M., 2005

[11] E. V. Ferapontov, Y. Nutku, 1994, arXiv: solv-int/94090004v1

[12] A. V. Kiselev, Fundamentalnaya i prikladnaya matematika, 12:7 (2006), 3 | Zbl

[13] I. A. Taimanov, Lektsii po differentsialnoi geometrii, Institut kompyuternykh issledovanii, M.–Izhevsk, 2002 | MR | Zbl

[14] M. Ablowitz, P. A. Clarcson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, NY, 1991 | MR | Zbl

[15] M. Gürses, 1997, arXiv: ; J. C. Brunelli, M. Gürses, K. Jeltukhin, 1999, arXiv: solv-int/9712018v1hep-th/9906233v1

[16] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | Zbl

[17] A. B. Borisov, V. V. Kisielev, Inverse Problems, 5 (1989), 959 | DOI | MR | Zbl

[18] E. Sh. Gutshabash, V. D. Lipovskii, Zap. nauchn. semin. LOMI, 180, 1990, 53 | Zbl

[19] B. Pelloni, Chastnoe soobschenie, Gallipoli, June 2008