Geodesic
Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 1, pp. 118-125 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a quadratic deformation of the Kowalevski top. This deformation includes a new integrable case for the Kirchhoff equations recently found by one of the authors as a degeneration. A $5\times 5$ matrix Lax pair for the deformed Kowalevski top is proposed. We also find similar deformations of the two-field Kowalevski gyrostat and the $so(p,q)$ Kowalevski top. All our Lax pairs are deformations of the corresponding Lax representations found by Reyman and Semenov–Tian-Shansky. A similar deformation of the Goryachev–Chaplygin top and its $3\times 3$ matrix Lax representation is also constructed. 
@article{TMF_2002_131_1_a9,
     author = {V. V. Sokolov and A. V. Tsiganov},
     title = {Lax {Pairs} for the {Deformed} {Kowalevski} and {Goryachev{\textendash}Chaplygin} {Tops}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {118--125},
     year = {2002},
     volume = {131},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_1_a9/}
}
TY  - JOUR
AU  - V. V. Sokolov
AU  - A. V. Tsiganov
TI  - Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 118
EP  - 125
VL  - 131
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_131_1_a9/
LA  - ru
ID  - TMF_2002_131_1_a9
ER  - 
%0 Journal Article
%A V. V. Sokolov
%A A. V. Tsiganov
%T Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 118-125
%V 131
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2002_131_1_a9/
%G ru
%F TMF_2002_131_1_a9
V. V. Sokolov; A. V. Tsiganov. Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 1, pp. 118-125. http://geodesic.mathdoc.fr/item/TMF_2002_131_1_a9/

[1] V. V. Sokolov, “A generalized Kowalevski Hamiltonian and new integrable cases on $e(3)$ and $so(4)$”, Kowalevski property, ed. V. B. Kuznetsov, 2002 ; CRM Proceedings and Lecture Notes, AMS (to appear); E-print nlin.SI/0110022 | MR

[2] V. V. Sokolov, TMF, 129:1 (2001), 31 | DOI | MR | Zbl

[3] A. I. Bobenko, A. G. Reyman, M. A. Semenov-Tian-Shansky, Commun. Math. Phys., 122 (1989), 321 | DOI | MR | Zbl

[4] D. Markushevich, J. Phys. A, 34 (2001), 2125 | DOI | MR | Zbl

[5] A. I. Bobenko, V. B. Kuznetsov, J. Phys. A, 21 (1988), 1999 | DOI | MR | Zbl

[6] Yu. B. Suris, Phys. Lett. A, 180 (1993), 419 | DOI | MR