Symmetries and Goursat problem for system of equations $u_{xy}=e^{u+v}u_y$, $v_{xy}=-e^{u+v}v_y$
Ufa mathematical journal, Tome 5 (2013) no. 3, pp. 20-27 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe the higher symmetries and construct the general solution for a hyperbolic system of equations. We also obtain the explicit formula for the solution of Goursat problem.
Keywords: symmetries, integrals.
Mots-clés : Goursat problem
@article{UFA_2013_5_3_a2,
     author = {Yu. G. Voronova and A. V. Zhiber},
     title = {Symmetries and {Goursat} problem for system of equations $u_{xy}=e^{u+v}u_y$, $v_{xy}=-e^{u+v}v_y$},
     journal = {Ufa mathematical journal},
     pages = {20--27},
     year = {2013},
     volume = {5},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2013_5_3_a2/}
}
TY  - JOUR
AU  - Yu. G. Voronova
AU  - A. V. Zhiber
TI  - Symmetries and Goursat problem for system of equations $u_{xy}=e^{u+v}u_y$, $v_{xy}=-e^{u+v}v_y$
JO  - Ufa mathematical journal
PY  - 2013
SP  - 20
EP  - 27
VL  - 5
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UFA_2013_5_3_a2/
LA  - en
ID  - UFA_2013_5_3_a2
ER  - 
%0 Journal Article
%A Yu. G. Voronova
%A A. V. Zhiber
%T Symmetries and Goursat problem for system of equations $u_{xy}=e^{u+v}u_y$, $v_{xy}=-e^{u+v}v_y$
%J Ufa mathematical journal
%D 2013
%P 20-27
%V 5
%N 3
%U http://geodesic.mathdoc.fr/item/UFA_2013_5_3_a2/
%G en
%F UFA_2013_5_3_a2
Yu. G. Voronova; A. V. Zhiber. Symmetries and Goursat problem for system of equations $u_{xy}=e^{u+v}u_y$, $v_{xy}=-e^{u+v}v_y$. Ufa mathematical journal, Tome 5 (2013) no. 3, pp. 20-27. http://geodesic.mathdoc.fr/item/UFA_2013_5_3_a2/

[1] Leznov A. N., Shabat A. B., “Usloviya obryva ryadov teorii vozmuschenii”, Integriruemye sistemy, BFAN SSSR, Ufa, 1982, 34–44

[2] Zhiber A. V., Mikhailova Yu. G., “Algoritm postroeniya obschego resheniya $n$-komponentnoi giperbolicheskoi sistemy uravnenii s nulevymi invariantami Laplasa i kraevye zadachi”, Ufimskii matematicheskii zhurnal, 1:3 (2009), 28–45 | Zbl

[3] Voronova Yu. G., “O zadache Koshi dlya lineinykh giperbolicheskikh sistem uravnenii s nulevymi obobschennymi invariantami Lalpalsa”, Ufimskii matematicheskii zhurnal, 2:2 (2010), 20–26 | Zbl

[4] Zhiber A. V., Mikhailova Yu. G., “O giperbolicheskikh sistemakh uravnenii s nulevymi obobschennymi invariantami Lalpalsa”, Trudy instituta matematiki i mekhaniki UrO RAN, 13, no. 4, 2007, 74–83

[5] Voronova Yu. G., “Postroenie resheniya zadachi Gursa dlya nelineinykh giperbolicheskikh uravnenii s integralami pervogo i vtorogo poryadka”, Mezhdunarodnaya shkola-konferentsiya dlya studentov, aspirantov i molodykh uchënykh, v. 1, BGU, Ufa, 2012, 51–58

[6] Gureva A. M., Metod kaskadnogo integrirovaniya Laplasa i nelineinye giperbolicheskie sistemy uravnenii, Dissertatsiya na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk, 2005, 172 pp.