Geodesic
Discrete Symmetries of the $n$-Wave Problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 132 (2002) no. 1, pp. 74-89 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show that discrete symmetries $T$ of multicomponent integrable systems have a fine structure and can be represented as products of positive integer powers of pairwise commuting basis discrete transformations $T_i$. The calculations are completed for the $n$-wave problem.
Keywords: integrable mappings and chains, higher-dimensional integrable systems.
Mots-clés : discrete transformations, Darboux transformation 
@article{TMF_2002_132_1_a3,
     author = {A. N. Leznov},
     title = {Discrete {Symmetries} of the $n${-Wave} {Problem}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {74--89},
     year = {2002},
     volume = {132},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_132_1_a3/}
}
TY  - JOUR
AU  - A. N. Leznov
TI  - Discrete Symmetries of the $n$-Wave Problem
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 74
EP  - 89
VL  - 132
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_132_1_a3/
LA  - ru
ID  - TMF_2002_132_1_a3
ER  - 
%0 Journal Article
%A A. N. Leznov
%T Discrete Symmetries of the $n$-Wave Problem
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 74-89
%V 132
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2002_132_1_a3/
%G ru
%F TMF_2002_132_1_a3
A. N. Leznov. Discrete Symmetries of the $n$-Wave Problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 132 (2002) no. 1, pp. 74-89. http://geodesic.mathdoc.fr/item/TMF_2002_132_1_a3/

[1] V. E. Zakharov, S. M. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov. Metod obratnoi zadachi rasseyaniya, Nauka, M., 1980 | MR

[2] A. N. Leznov, TMF, 73:2 (1987), 302 | MR

[3] A. N. Leznov, Backlund transformation for the self-dual Yang–Mills equations, Preprint IHEP 91-45, IHEP, Protvino, 1991; The solution of discrete symmetry equations for four-dimensional self-dual system in the case of arbitrary semisimple gauge algebra, Preprint MPI-40, MPI, Bonn, 1996

[4] A. N. Leznov, EChAYa, 27:5 (1996), 1161 | MR

[5] A. N. Leznov, T. A. Yuzbashyan, Phys. Lett. A, 242:1–2 (1998), 31 | DOI | MR | Zbl

[6] C. N. Yang, Phys. Rev. Lett., 38 (1977), 1377 | DOI | MR

[7] A. N. Leznov, TMF, 122:2 (2000), 251 ; 117:1 (1998), 107 | DOI | MR | Zbl | DOI | MR | Zbl