107 research outputs found
Monodromy approach to the scaling limits in the isomonodromy systems
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.Comment: Latex, 15 pages, 1 figure; submitted to the proceedings of the
conference NEEDS 2002; in compare to the original version, there are minor
changes in the references and in the main body of the articl
Quasi-linear Stokes phenomenon for the second Painlev\'e transcendent
Using the Riemann-Hilbert approach, we study the quasi-linear Stokes
phenomenon for the second Painlev\'e equation . The
precise description of the exponentially small jump in the dominant solution
approaching as is given. For the asymptotic power
expansion of the dominant solution, the coefficient asymptotics is found.Comment: 19 pages, LaTe
Quasi-linear Stokes phenomenon for the Painlev\'e first equation
Using the Riemann-Hilbert approach, the -function corresponding to the
solution of the first Painleve equation, , with the asymptotic
behavior as is constructed. The
exponentially small jump in the dominant solution and the coefficient
asymptotics in the power-like expansion to the latter are found.Comment: version accepted for publicatio
On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev\'e equation
Using a simple operator-norm estimate we show that the solution to the second
Painlev\'e equation within the Ablowitz-Segur family is pole-free in a well
defined region of the complex plane of the independent variable. The result is
illustrated with several numerical examples.Comment: 8 pages, to appear in Nonlinearit
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