0000000000653170
AUTHOR
Sverrir Olafsson
Integrability Conditions: Recent Results in the Theory of Integrable Models
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…
Statistical mechanics of the NLS models and their avatars
“In Vishnuland what avatar? Or who in Moscow (Leningrad) towards the czar [1]”. The different manifestations (avatars) of the Nonlinear Schrodinger equation (NLS models) are described including both classical and quantum integrable cases. For reasons explained the sinh-Gordon and sine-Gordon models, which can be interpreted as covariant manifestations of the ‘repulsive’ and ‘attractive’ NLS models, respectively, are chosen as generic models for the statistical mechanics. It is shown in the text how the quantum and classical free energies can be calculated by a method of functional integration which uses the classical action-angle variables on the real line with decaying boundary conditions,…