On the Lax pairs for the generalized Kowalewski and Goryachev-Chaplygin tops
نویسنده
چکیده
A polynomial deformation of the Kowalewski top is considered. This deformation includes as a degeneration a new integrable case for the Kirchhoff equations found recently by one of the authors. A 5× 5 matrix Lax pair for the deformed Kowalewski top is proposed. Also deformations of the two-field Kowalewski gyrostat and the so(p, q) Kowalewski top are found. All our Lax pairs are deformations of the corresponding Lax representations found by Reyman and Semenov-Tian Shansky. In addition, a similar deformation of the Goryachev-Chaplygin top and its 3× 3 matrix Lax representation is constructed.
منابع مشابه
Simultaneous separation for the Kowalevski and Goryachev-Chaplygin gyrostats
In the special case of zero square integral the Kowalevski gyrostat and Goryachev-Chaplygin gyrostat share a simple separation of variables originated from the 4× 4 Lax matrix. EPSRC Advanced Research Fellow
متن کاملIntegrable Models, Susy Gauge Theories and String Theory
We consider the close relation between duality in N = 2 SUSY gauge theories and integrable models. Various integrable models ranging from Toda lattices, Calogero models, spinning tops, and spin chains are related to the quantum moduli space of vacua of N = 2 SUSY gauge theories. In particular, SU(3) gauge theories with two flavors of massless quarks in the fundamental representation can be rela...
متن کاملOn the case of Goryachev - Chaplygin and new examples of integrable conservative systems on S 2 Elena
The aim of this paper is to describe a class of conservative systems on S possessing an integral cubic in momenta. We prove that this class of systems consists off the case of Goryachev-Chaplygin, the one-parameter family of systems which has been found by the author in the previous paper and a new two-parameter family of conservative systems on S possessing an integral cubic in momenta.
متن کاملGeneralization of the Goryachev – Chaplygin Case
In this paper we present a generalization of the Goryachev –Chaplygin integrable case on a bundle of Poisson brackets, and on Sokolov terms in his new integrable case of Kirchhoff equations. We also present a new analogous integrable case for the quaternion form of rigid body dynamics’ equations. This form of equations is recently developed and we can use it for the description of rigid body mo...
متن کاملTrivially related lax pairs of the Sawada-Kotera equation
We show that a recently introduced Lax pair of the Sawada-Kotera equation is nota new one but is trivially related to the known old Lax pair. Using the so-called trivialcompositions of the old Lax pairs with a differentially constrained arbitrary operators,we give some examples of trivial Lax pairs of KdV and Sawada-Kotera equations.
متن کامل