1,664 research outputs found
On the Reductions and Classical Solutions of the Schlesinger equations
The Schlesinger equations describe monodromy preserving
deformations of order Fuchsian systems with poles. They can be
considered as a family of commuting time-dependent Hamiltonian systems on the
direct product of copies of matrix algebras equipped with the
standard linear Poisson bracket. In this paper we address the problem of
reduction of particular solutions of ``more complicated'' Schlesinger equations
to ``simpler'' having or .Comment: 32 pages. To the memory of our friend Andrei Bolibruc
Frobenius manifold structures on the spaces of abelian integrals
Frobenius manifold structures on the spaces of abelian integrals were
constructed by I. Krichever. We use D-modules, deformation theory, and
homological algebra to give a coordinate-free description of these structures.
It turns out that the tangent sheaf multiplication has a cohomological origin,
while the Levi-Civita connection is related to 1-dimensional isomonodromic
deformations.Comment: Expanded version. The case of an abelian integral with multiple poles
is treated. Other minor improvements. Final versio
The Extended Bigraded Toda hierarchy
We generalize the Toda lattice hierarchy by considering N+M dependent
variables. We construct roots and logarithms of the Lax operator which are
uniquely defined operators with coefficients that are -series of
differential polynomials in the dependent variables, and we use them to provide
a Lax pair definition of the extended bigraded Toda hierarchy. Using R-matrix
theory we give the bihamiltonian formulation of this hierarchy and we prove the
existence of a tau function for its solutions. Finally we study the
dispersionless limit and its connection with a class of Frobenius manifolds on
the orbit space of the extended affine Weyl groups of the series.Comment: 32 pages, corrected typo
Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model Embedding
We investigate SU(2) gauge fields topology using new approach, which exploits
the well known connection between SU(2) gauge theory and quaternionic
projective sigma-models and allows to formulate the topological charge density
entirely in terms of sigma-model fields. The method is studied in details and
for thermalized vacuum configurations is shown to be compatible with
overlap-based definition. We confirm that the topological charge is distributed
in localized four dimensional regions which, however, are not compatible with
instantons. Topological density bulk distribution is investigated at different
lattice spacings and is shown to possess some universal properties.Comment: revtex4, 19 pages (24 ps figures included); replaced to match the
published version, to appear in PRD; minor changes, references adde
Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems
Rational Lax hierarchies introduced by Krichever are generalized. A
systematic construction of infinite multi-Hamiltonian hierarchies and related
conserved quantities is presented. The method is based on the classical
R-matrix approach applied to Poisson algebras. A proof, that Poisson operators
constructed near different points of Laurent expansion of Lax functions are
equal, is given. All results are illustrated by several examples.Comment: 28 page
Solution of the dispersionless Hirota equations
The dispersionless differential Fay identity is shown to be equivalent to a
kernel expansion providing a universal algebraic characterization and solution
of the dispersionless Hirota equations. Some calculations based on D-bar data
of the action are also indicated.Comment: Late
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