Search results for "Monodromy matrix"

showing 2 items of 2 documents

Integrability Conditions: Recent Results in the Theory of Integrable Models

1990

This paper reports various results achieved recently in the theory of integrable models. These are summarised in the Fig.1! At the Chester meeting [1] two of the authors were concerned [1] with the local Riemann-Hilbert problem (double-lined box in the centre of Fig.1), its limit as a non-local Riemann-Hilbert problem used to solve classical integrable models in 2+1 dimensions (two space and one time dimensions) [2,3], and the connection of this Riemann-Hilbert problem with Ueno’s [4] Riemann-Hilbert problem associated with the representation of the algebra gl(∞) in terms of Z⊗Z matrices (Z the integers) and the solution of the K-P equations in 2+1. We were also concerned [1] with the const…

Loop (topology)Pure mathematicsIntegrable systemQuantum groupLie algebraMonodromy matrixConnection (algebraic framework)Hopf algebraSymplectic manifoldMathematics
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Classical and Quantum Nonultralocal Systems on the Lattice

1997

We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix. A nonultralocal quantum algebras on the lattices for these systems are constructed. For some class of such algebras an ultralocalization procedure is proposed. The technique of the modified Bethe-Anzatz for these algebras is developed and is applied to the nonlinear sigma model problem.

PhysicsPoisson bracketNonlinear systemPure mathematicsNonlinear Sciences::Exactly Solvable and Integrable SystemsSigma modelPoisson manifoldLattice (order)Quantum mechanicsMonodromy matrixQuantumPoisson algebra
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