Geodesic
Lax Pairs for the Deformed Kowalevski and Goryachev--Chaplygin Tops
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 1, pp. 118-125

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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--Chaplygin} {Tops}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {118--125},
     publisher = {mathdoc},
     volume = {131},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_1_a9/}
}
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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/