Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops

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.