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Separation of variables for the classical elliptic reflection equation algebra.
- Source :
-
Nuclear Physics B . Mar2024, Vol. 1000, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- In the present paper we construct separation of variables (SoV) for all Lax-integrable systems, two by two Lax matrix of which enjoys classical reflection equation algebra with the elliptic r − s matrices. We show that, similar to the cases of SoV for the classical XYZ and XXZ models [1,2] , the constructed SoV admits two types of momenta, which are important in the quantum case [1,2]. We consider two examples of such the integrable hamiltonian systems governed by the simplest Poisson brackets connected with classical reflection equation algebra with the elliptic r − s matrices. They are the classical Sklyanin algebra and its four-dimensional extension which provide a quadratic structure for the classical Steklov top. We explicitly construct the variables of separation, Abel equations and reconstruction formulae for the corresponding integrable models. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 05503213
- Volume :
- 1000
- Database :
- Academic Search Index
- Journal :
- Nuclear Physics B
- Publication Type :
- Academic Journal
- Accession number :
- 175849807
- Full Text :
- https://doi.org/10.1016/j.nuclphysb.2024.116460