916 research outputs found
Lax matrices for Yang-Baxter maps
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical
solutions to the quantum Yang-Baxter equation) the Lax representation can be
derived straight from the map itself. A similar phenomenon for 3D consistent
equations on quad-graphs has been recently discovered by A. Bobenko and one of
the authors, and by F. Nijhoff
Algebraic Solutions of the Multicomponent KP Hierarchy
It is shown that it is possible to write down tau functions for the
-component KP hierarchy in terms of non-abelian theta functions. This is a
generalization of the rank 1 situation; that is, the relation of theta
functions of Jacobians and tau functions for the KP hierarchy.Comment: 19 page
Vector bundles and Lax equations on algebraic curves
The Hamiltonian theory of zero-curvature equations with spectral parameter on
an arbitrary compact Riemann surface is constructed. It is shown that the
equations can be seen as commuting flows of an infinite-dimensional field
generalization of the Hitchin system. The field analog of the elliptic
Calogero-Moser system is proposed. An explicit parameterization of Hitchin
system based on the Tyurin parameters for stable holomorphic vector bundles on
algebraic curves is obtained.Comment: Latex, 42page
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