We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic so(3) ⊗ so(3) -valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the “separating functions” B(u) and A(u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Euler’s top, Steklov–Lyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and “spin” generalization of Steklov–Lyapunov model.

Skrypnyk, T. (2017). Separation of variables in anisotropic models and non-skew-symmetric elliptic r-matrix. LETTERS IN MATHEMATICAL PHYSICS, 107(5), 793-819 [10.1007/s11005-016-0920-0].

Separation of variables in anisotropic models and non-skew-symmetric elliptic r-matrix

Skrypnyk, T
2017

Abstract

We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic so(3) ⊗ so(3) -valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the “separating functions” B(u) and A(u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Euler’s top, Steklov–Lyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and “spin” generalization of Steklov–Lyapunov model.
Articolo in rivista - Articolo scientifico
Classical r-matrices; Integrable systems; Separation of variables; Statistical and Nonlinear Physics; Mathematical Physics
English
2017
107
5
793
819
none
Skrypnyk, T. (2017). Separation of variables in anisotropic models and non-skew-symmetric elliptic r-matrix. LETTERS IN MATHEMATICAL PHYSICS, 107(5), 793-819 [10.1007/s11005-016-0920-0].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/189900
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