4 citations · 13 across the 8 of their papers we have counts for
9 papers · 1 filter
The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz
Taras Skrypnyk
We show that the Lipkin-Meshkov-Glick -fermion model is a particular case of one-spin Gaudin-type model in an external magnetic field corresponding to a limiting case of non-sk…
Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models
Taras Skrypnyk
We construct two new one-parametric families of separated variables for the classical Lax-integrable Hamiltonian systems governed by a one-parametric family of non-skew-symmetric,…
A new approach to separation of variables for the Clebsch integrable system. Part II: Inversion of the Abel--Prym map
Yu. Fedorov, F. Magri, T. Skrypnyk
This is the second part of a paper describing a new concept of separation of variables applied to the classical Clebsch integrable case. The quadratures obtained in Part I (also up…
A new approach to separation of variables for the Clebsch integrable system. Part I: Reduction to quadratures
Yu. Fedorov, F. Magri, T. Skrypnyk
This is the first part of a two-part paper describing a new concept of separation of variables applied to the Clebsch integrable case of the Kirchhoff equations. There are two prin…
Classical double, R-operators and negative flows of integrable hierarchies
B. Dubrovin, T. Skrypnyk
Using classical double G of a Lie algebra g equipped with a classical R-operator we define two sets of mutually commuting functions with respect to the initial Lie-Poisson bracket…
Classical R-Operators and Integrable Generalizations of Thirring Equations
Taras V. Skrypnyk
We construct different integrable generalizations of the massive Thirring equations corresponding loop algebras in different gradings and associated ''…