# Meromorphy of solutions for a wide class of ordinary differential equations of Painlev\'e type

@inproceedings{Domrin2021MeromorphyOS, title={Meromorphy of solutions for a wide class of ordinary differential equations of Painlev\'e type}, author={A. V. Domrin and M. A. Shumkin and Bulat Irekovich Suleimanov}, year={2021} }

where z0, a and b are any complex constants. The Painlevé ODE are currently being applied to a wide variety of problems in mathematics and mathematical physics. But the problem of rigorously proving the absence of nonpolar movable singularities of their solutions turned out to be difficult. Original proofs by Painlevé and his followers appeared to be incomplete. Gaps were also found in a number of subsequent attempts to give a satisfying proof. The meromorphy of all solutions of the simplest…

## References

SHOWING 1-10 OF 92 REFERENCES

Global Meromorphy of Solutions of the Painlevé Equations and Their Hierarchies

- Mathematics
- 2020

We show that all local holomorphic solutions of all equations constituting the hierarchies of the first and second Painleve equations can be analytically continued to meromorphic functions on the…

Meromorphic extension of solutions of soliton equations

- Mathematics
- 2010

We consider local versions of the direct and inverse scattering transforms and describe their analytic properties, which are analogous to the properties of the classical Laplace and Borel transforms.…

On holomorphic solutions of equations of Korteweg–de Vries type

- Mathematics
- 2013

We show that, for any of the equations indicated in the title, every solution locally holomorphic in x and t admits global meromorphic continuation in x for each t with trivial monodromy at each…

Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation

- 2019

In this paper we prove that a degenerate Gamier system of (9/2)-type has the Painlev6 property. The restriction of the system to a complex line gives an example of a fourth order non-linear ordinary…

Turning Points of Linear Systems and Double Asymptotics of the Painlevé Transcendents

- Mathematics
- 1995

Recently, on the basis of the isomonodromy deformation method (IDM) [1], a considerable success has been achieved in the description of asymptotic properties of the Painleve transcendents especially…

Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation

- Physics, Mathematics
- 2021

We provide a general solution for a first order ordinary differential equation with a rational right-hand side, which arises in constructing asymptotics for large time of simultaneous solutions of…

Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2019

We prove that there exists the unique odd meromorphic solution of dP3, $u(\tau)$ such that $u(0)=0$, and study some of its properties, mainly: the coefficients of its Taylor expansion at the origin…

The existence of a real pole-free solution of the fourth order analogue of the Painleve I equation

- Mathematics, Physics
- 2007

We establish the existence of a real solution y( x, T) with no poles on the real line of the following fourth order analogue of the Painleve I equation: x = T y - (1/6y(3) + 1/24(y(x)(2) +2yy(xx)) +…

THE LAX PAIR FOR THE MKDV HIERARCHY

- Mathematics
- 2006

Rational solutions of the second, third and fourth Painleve equations (-) can be expressed in terms of logarithmic derivatives of special polynomials that are defined through coupled second order,…

On an isomonodromy deformation equation without the Painlevé property

- Mathematics, Physics
- 2014

We show that the fourth-order nonlinear ODE which controls the pole dynamics in the general solution of equation PI2 compatible with the KdV equation exhibits two remarkable properties: (1) it…