A global factorization theorem for the ZS-AKNS system.
A Lax formalism for the elliptic difference Painlevé equation.
A particular solution of a Painlevé system in terms of the hypergeometric function .
A simple proof of the non-integrability of the first and the second Painlevé equations
The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.
An ultradiscrete matrix version of the fourth Painlevé equation.
Application of uniform asymptotics method to analyzing the asymptotic behaviour of the general fourth Painlevé transcendent.
Asymptotic expansions of solutions to the fifth Painlevé equation in neighbourhoods of singular and nonsingular points of the equation
Applying methods of plane Power Geometry we are looking for the asymptotic expansions of solutions to the fifth Painlevé equation in the neighbourhood of its singular and nonsingular points.