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N. Kudryashov (1999)
TRANSCENDENTS DEFINED BY NONLINEAR FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONSJournal of Physics A, 32
N. Kudryashov (1998)
On new transcendents defined by nonlinear ordinary differential equationsJournal of Physics A, 31
M. Ablowitz, A. Ramani, H. Segur (1980)
A connection between nonlinear evolution equations and ordinary differential equations of P‐type. IIJournal of Mathematical Physics, 21
N. Kudryashov (1997)
The second Painlevé equation as a model for the electric field in a semiconductorPhysics Letters A, 233
V. Gromak, I. Laine, S. Shimomura (2002)
Painlev'e di erential equations in the complex plane
N. Kudryashov (2019)
Rational and Special Solutions for Some Painlevé HierarchiesRegular and Chaotic Dynamics, 24
Wolfgang Hackbusch (2014)
Ordinary Differential Equations
J. Weiss (1983)
THE PAINLEVE PROPERTY FOR PARTIAL DIFFERENTIAL EQUATIONS. II. BACKLUND TRANSFORMATION, LAX PAIRS, AND THE SCHWARZIAN DERIVATIVEJournal of Mathematical Physics, 24
H. Umemura (1990)
Second proof of the irreducibility of the first differential equation of painlevéNagoya Mathematical Journal, 117
J. Weiss (1984)
On classes of integrable systems and the Painlevé propertyJournal of Mathematical Physics, 25
N. Kudryashov (2002)
One generalization of the second Painlevé hierarchyJournal of Physics A: Mathematical and General, 35
(1971)
On the Theory of Painlevé's Second Equation
N. Kudryashov (2014)
Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchiesRegular and Chaotic Dynamics, 19
M. Ablowitz, H. Segur (1977)
Exact Linearization of a Painlevé TranscendentPhysical Review Letters, 38
N. Kudryashov (2020)
Lax Pairs and Special Polynomials Associated with Self-similar Reductions of Sawada — Kotera and Kupershmidt EquationsRegular and Chaotic Dynamics, 25
N. Kudryashov (2003)
Amalgamations of the Painlevé EquationsTheoretical and Mathematical Physics, 137
A. Borisov, N. Kudryashov (2014)
Paul Painlevé and his contribution to scienceRegular and Chaotic Dynamics, 19
P. Painlevé (1902)
Sur les équations différentielles du second ordre et d'ordre supérieur dont l'intégrale générale est uniformeActa Mathematica, 25
N. Kudryashov, A. Pickering (1998)
Rational solutions for Schwarzian integrable hierarchiesJournal of Physics A, 31
A. Pickering (2002)
Coalescence limits for higher order Painlevé equationsPhysics Letters A, 301
N. Kudryashov (1997)
The first and second Painlevé equations of higher order and some relations between themPhysics Letters A, 224
M. Ablowitz, P. Clarkson (1992)
Solitons, Nonlinear Evolution Equations and Inverse Scattering
Nonlinear differential equations associated with the second Painlevé equation are considered. Transformations for solutions of the singular manifold equation are presented. It is shown that rational solutions of the singular manifold equation are determined by means of the Yablonskii-Vorob’ev polynomials. It is demonstrated that rational solutions for some differential equations are also expressed via the Yablonskii-Vorob’ev polynomials.
Regular and Chaotic Dynamics – Springer Journals
Published: May 31, 2020
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