Monodromy approach to the scaling limits in the isomonodromy systems

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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Latex, 15 pages, 1 figure; submitted to the proceedings of the conference NEEDS 2002; in compare to the original version, ther

Scientific paper

10.1023/B:TAMP.0000007917.73394.

The isomonodromy deformation method is applied to the scaling limits in the linear NxN matrix equations with rational coefficients to obtain the deformation equations for the algebraic curves which describe the local behavior of the reduced versions for the relevant isomonodromy deformation equations. The approach is illustrated by the study of the algebraic curve associated to the n-large asymptotics in the sequence of the bi-orthogonal polynomials with cubic potentials.

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