Neste trabalho estudamos a relação entre os coeficientes da relação de recorrência de alguns polinômios ortogonais semiclássicos e as equações discretas de Painlevé. Para isso considera­mos uma propriedade importante de ...

The theory of Painleve equations is first explained in the historical context of the creation of new equations from the singularity analysis on the complex plane. The study of the SL(N) mKdV hierarchy results in the theory ...

This paper rst discusses irreducibility of a Painlev e equation P. We explain how the Painlev e property is helpful for the computation of special classical and algebraic solutions. As in a paper of Morales-Ruiz we ...

We extend Painlevé IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlevé IV and II equations for special limits of the underlying ...

We identify the self-similarity limit of the second flow of sl(N)mKdVhierarchy with the periodic dressing chain thus establishing a connection to A(1) N-1 invariant Painlev'e equations. The A(1) N-1 Bcklund symmetries of ...

A mixed symmetric Painlevé III-V model which describes a hybrid of both equations is defined and obtained by successive self-similarity and Dirac Lagrange multiplier reductions from an integrable 4-boson hierarchy.

The current work aims at applications of mathematical methods of Painlevé integrability in physics, on the other side it also approaches the integrable hierarchies formalism and the 2M-bose model where differential equations ...

We review the construction of the mixed Painlevé P III –V system in terms of a 4-boson integrable model and discuss its symmetries. Such a mixed system consist of a hybrid differential equation that for special limits of ...

We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyse relations between the matrix coefficients of the three term relations for the orthonormal polynomials ...

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient ...