Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2002-11-15
Theor.Math.Phys. 137 (2003) 1691-1702; Teor.Mat.Fiz. 137 (2003) 393-407
Nonlinear Sciences
Exactly Solvable and Integrable Systems
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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