Polynomial Hamiltonians associated with Painlevé equations, I
نویسندگان
چکیده
منابع مشابه
On Discrete Painlevé Equations Associated with the Lattice Kdv Systems and the Painlevé Vi Equation
1 Abstract A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painlevé V equation. Its derivation is based on the similarity reduction on the two-dimensional lattice of integrable partial difference equations of KdV type. The new equation which is referred to as GDP (generalised discrete Painlevé equation) ...
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— The paper consists of two parts. In the first part, we explain an excellent idea, due to mathematicians of the 19-th century, of naturally developing classical Galois theory of algebraic equations to an infinite dimensional Galois theory of nonlinear differential equations. We show with an instructive example how we can realize the idea of the 19-th century in a rigorous framework. In the sec...
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— Time independent Hamiltonians of the physical type H = (P 2 1 + P 2 2 )/2 + V (Q1, Q2) pass the Painlevé test for only seven potentials V , known as the Hénon-Heiles Hamiltonians, each depending on a finite number of free constants. Proving the Painlevé property was not yet achieved for generic values of the free constants. We integrate each missing case by building a birational transformatio...
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By means of geometrical classification ([22]) of space of initial conditions, it is natural to consider the three types, PIII(D6), PIII(D7) and PIII(D8), for the third Painlevé equation. The fourth article of the series of papers [17] on the Painlevé equations is concerned with PIII(D6), generic type of the equation. The other two types, PIII(D7) and PIII(D8) are obtained as degeneration from P...
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The discrete Painlevé I equation (dPI) is an integrable difference equation which has the classical first Painlevé equation (PI) as a continuum limit. dPI is believed to be integrable because it is the discrete isomonodromy condition for an associated (single-valued) linear problem. In this paper, we derive higher-order difference equations as isomonodromy conditions that are associated to the ...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1980
ISSN: 0386-2194
DOI: 10.3792/pjaa.56.264