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Rational Solutions to dPIV
 in Proceedings of the Second Workshop on Symmetries and Integrability of Difference Equations
, 1999
"... We study the rational solutions of the discrete version of Painlevé’s fourth equation (dPIV). The solutions are generated by applying Schlesinger transformations on the seed solutions −2z and −1/z. After studying the structure of these solutions we are able to write them in a determinantal form tha ..."
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Cited by 1 (1 self)
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We study the rational solutions of the discrete version of Painlevé’s fourth equation (dPIV). The solutions are generated by applying Schlesinger transformations on the seed solutions −2z and −1/z. After studying the structure of these solutions we are able to write them in a determinantal form
Polynomial and rational solutions of holonomic systems
 n o 12
"... Polynomial and rational solutions for linear ordinary differential equations can be obtained by algorithmic methods. For instance, the maple package DEtools provides efficient functions polysols and ratsols to find polynomial and rational ..."
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Cited by 17 (5 self)
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Polynomial and rational solutions for linear ordinary differential equations can be obtained by algorithmic methods. For instance, the maple package DEtools provides efficient functions polysols and ratsols to find polynomial and rational
Rational Solutions of Linear Difference Equations
 In Proceedings of ISSAC’98
, 1998
"... This paper presents a new and sharper bound for denominators of rational solutions of linear difference and qdifference equations. This can be used to compute rational solutions more efficiently. 1 Introduction Let be the Cautomorphism of C(x) defined by (x) = x + 1. In this paper we will consid ..."
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Cited by 22 (1 self)
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This paper presents a new and sharper bound for denominators of rational solutions of linear difference and qdifference equations. This can be used to compute rational solutions more efficiently. 1 Introduction Let be the Cautomorphism of C(x) defined by (x) = x + 1. In this paper we
Rational solutions to the PainlevéVI equation
 MATH. ANNALEN
"... In this paper, we classify all values of the parameters α, β, γ and δ of the Painlevé VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlevé VI equation. ..."
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Cited by 1 (0 self)
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In this paper, we classify all values of the parameters α, β, γ and δ of the Painlevé VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlevé VI equation.
Approximated Rational Solutions for Systems of Differential
"... In [3] we presented a technique to study the existence of rational solutions for systems of linear firstorder ordinary differential equations. The method is based on a rationality characterisation that involves Matrix Padé Approximants. Moreover the main ideas were only applied in the numerical res ..."
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In [3] we presented a technique to study the existence of rational solutions for systems of linear firstorder ordinary differential equations. The method is based on a rationality characterisation that involves Matrix Padé Approximants. Moreover the main ideas were only applied in the numerical
Rational Solutions of the A (1) 5 Painlevé Equation
, 2009
"... We completely classify all of rational solutions of the A (1) 5 Painlevé equation, which is a generalization of the fifth Painlevé equation. The rational solutions are classified to five types by the Bäcklund transformation group. ..."
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Cited by 1 (1 self)
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We completely classify all of rational solutions of the A (1) 5 Painlevé equation, which is a generalization of the fifth Painlevé equation. The rational solutions are classified to five types by the Bäcklund transformation group.
Rational Solutions of the A (1) 4 Painlevé Equation
, 2009
"... We completely classify all of rational solutions of the A (1) 4 Painlevé equation, which is a generalization of the fourth Painlevé equation. The rational solutions are classified to three by the Bäcklund transformation group. ..."
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Cited by 1 (1 self)
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We completely classify all of rational solutions of the A (1) 4 Painlevé equation, which is a generalization of the fourth Painlevé equation. The rational solutions are classified to three by the Bäcklund transformation group.
Rational solutions to a KdVlike equation
"... a b s t r a c t Two classes of rational solutions to a KdVlike nonlinear differential equation are constructed. The basic object is a generalized bilinear differential equation based on a prime number p ¼ 3. A conjecture is made that the two presented classes of rational solutions contain all rati ..."
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a b s t r a c t Two classes of rational solutions to a KdVlike nonlinear differential equation are constructed. The basic object is a generalized bilinear differential equation based on a prime number p ¼ 3. A conjecture is made that the two presented classes of rational solutions contain all
Finding rational solutions of rational systems of autonomous ODEs
"... In this paper we provide an algorithm to find explicitly rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its invariant algebraic curves. The method is based on the rational parametrization of the rational invariant algebraic curves and intensively us ..."
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In this paper we provide an algorithm to find explicitly rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its invariant algebraic curves. The method is based on the rational parametrization of the rational invariant algebraic curves and intensively
Rational Heuristics for Rational Solutions of Riccati Equations
"... We describe some new algorithm and heuristics for computing the polynomial and rational solutions of bounded degree of a class of ordinary differential equations, which includes generalized Riccati equations. As a consequence, our methods can be used for factoring linear ordinary differential equati ..."
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We describe some new algorithm and heuristics for computing the polynomial and rational solutions of bounded degree of a class of ordinary differential equations, which includes generalized Riccati equations. As a consequence, our methods can be used for factoring linear ordinary differential
Results 1  10
of
4,453