360 research outputs found
Symmetric solutions to dispersionless 2D Toda hierarchy, Hurwitz numbers and conformal dynamics
We explicitly construct the series expansion for a certain class of solutions
to the 2D Toda hierarchy in the zero dispersion limit, which we call symmetric
solutions. We express the Taylor coefficients through some universal
combinatorial constants and find recurrence relations for them. These results
are used to obtain new formulas for the genus 0 double Hurwitz numbers. They
can also serve as a starting point for a constructive approach to the Riemann
mapping problem and the inverse potential problem in 2D.Comment: 26 page
Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz
We consider GL(K|M)-invariant integrable supersymmetric spin chains with
twisted boundary conditions and elucidate the role of Backlund transformations
in solving the difference Hirota equation for eigenvalues of their transfer
matrices. The nested Bethe ansatz technique is shown to be equivalent to a
chain of successive Backlund transformations "undressing" the original problem
to a trivial one.Comment: 22 pages, 2 figures, based on the talk given at the Workshop
"Classical and Quantum Integrable Systems", Dubna, January 200
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