96 citations · 820 across the 46 of their papers we have counts for
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Solitons in a 3d integrable model
S. Sergeev
Equations of motion for a classical 3d discrete model, whose auxialiary system is a linear system, are investigated. The Lagrangian form of the equations of motion is derived. The…
Quantum 2+1 evolution model
S. M. Sergeev
A quantum evolution model in 2+1 discrete space - time, connected with 3D fundamental map R, is investigated. Map R is derived as a map providing a zero curvature of a two dimensio…
3D symplectic map
S. M. Sergeev
Quantum 3D R-matrix in the classical (i.e. functional) limit gives a symplectic map of dynamical variables. The corresponding 3D evolution model is considered. An auxiliary problem…
Functional Tetrahedron Equation
R. M. Kashaev, I. G. Korepanov, S. M. Sergeev
We describe a scheme of constructing classical integrable models in 2+1-dimensional discrete space-time, based on the functional tetrahedron equation - equation that makes manifest…
On a two dimensional system associated with the complex of the solutions of the Tetrahedron equation
S. M. Sergeev
A sort of two dimensional linear auxiliary problem for the complex of 3D -- operators associated with the Zamolodchikov -- Bazhanov -- Baxter statistical model is proposed. Thi…
Solutions of the functional tetrahedron equation connected with the local Yang -- Baxter equation for the ferro-electric
S. M. Sergeev
Local (or modified) Yang -- Baxter equation (LYBE) gives the functional map from the parameters of the weights in the left hand side to the parameters of the correspondent weights…