Finite-dimensional reductions of the discrete Toda chain

Details Finite-dimensional reductions of the discrete Toda chain Finite-dimensional reductions of the discrete Toda chain

2004-03-10

arxiv.org/abs/nlin/0403015v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Submitted to Jornal of Physics A: Math. Gen., 14 pages

Scientific paper

10.1088/0305-4470/37/33/008

The problem of construction of integrable boundary conditions for the
discrete Toda chain is considered. The restricted chains for properly chosen
closure conditions are reduced to the well known discrete Painlev\'e equations
$dP_{III}$, $dP_{V}$, $dP_{VI}$. Lax representations for these discrete
Painlev\'e equations are found.

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