Geodesic
Graded Lie algebras, representation theory, integrable mappings, and integrable systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 2, pp. 251-271

Voir la notice de l'article provenant de la source Math-Net.Ru

A new class of integrable mappings and chains is introduced. The corresponding $1+2$ integrable systems that are invariant under such integrable mappings are presented in an explicit form. Soliton-type solutions of these systems are constructed in terms of matrix elements of fundamental representations of semisimple $A_n$ algebras for a given group element. The possibility of generalizing this construction to the multidimensional case is discussed. 
@article{TMF_2000_122_2_a8,
     author = {A. N. Leznov},
     title = {Graded {Lie} algebras, representation theory, integrable mappings, and integrable systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {251--271},
     publisher = {mathdoc},
     volume = {122},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_122_2_a8/}
}
TY  - JOUR
AU  - A. N. Leznov
TI  - Graded Lie algebras, representation theory, integrable mappings, and integrable systems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2000
SP  - 251
EP  - 271
VL  - 122
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2000_122_2_a8/
LA  - ru
ID  - TMF_2000_122_2_a8
ER  - 
%0 Journal Article
%A A. N. Leznov
%T Graded Lie algebras, representation theory, integrable mappings, and integrable systems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2000
%P 251-271
%V 122
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2000_122_2_a8/
%G ru
%F TMF_2000_122_2_a8
A. N. Leznov. Graded Lie algebras, representation theory, integrable mappings, and integrable systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 2, pp. 251-271. http://geodesic.mathdoc.fr/item/TMF_2000_122_2_a8/