Results 21 to 30 of about 8,283 (176)

Darboux polynomials, balances and Painlevé property [PDF]

Regular and Chaotic Dynamics, 2017
For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of the system and the Painlevé property. As far as we know, these are the first results which relate the Darboux theory of integrability, first, to the Painlevé property and, second, to the Kovalevskaya ...
Llibre, Jaume, Valls, Clàudia
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Homogeneous darboux polynomials and generalising integrable ODE systems

Journal of Computational Dynamics, 2021
We show that any system of ODEs can be modified whilst preserving its homogeneous Darboux polynomials. We employ the result to generalise a hierarchy of integrable Lotka-Volterra systems.
van der Kamp, Peter H., McLaren, D. I., Quispel, G. R. W.   +2 more
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Darboux and rational first integrals for a family of cubic three dimensional system

Zanco Journal of Pure and Applied Sciences, 2021
In this paper, we investigate the first integrals of the following system   where  and , . This kind of system is a special case of three-dimensional polynomial cubic differential systems.
Sarbast H. Mikaeel , Azad I. Amen
doaj  

Asymptotics of Meixner polynomials and Christoffel–Darboux kernels [PDF]

Transactions of the Moscow Mathematical Society, 2013
Summary: We obtain the asymptotics of the classical Meixner polynomials \(M_n(x)\) (orthogonal with respect to a discrete measure supported at the nonnegative integer points) and the corresponding reproducing kernels (Christoffel-Darboux kernels) \(K_n(x,y)\) as \(n\) and the variable \(x\) tend to infinity under various relationships between their ...
Aptekarev, A. I., Tulyakov, D. N.
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Asymptotic behaviour of zeros of exceptional Jacobi and Laguerre polynomials [PDF]

, 2012
The location and asymptotic behaviour for large n of the zeros of exceptional Jacobi and Laguerre polynomials are discussed. The zeros of exceptional polynomials fall into two classes: the regular zeros, which lie in the interval of orthogonality and the
Adler, Bochner, Bueno, Clarkson, Clarkson, Crum, Darboux, David Gómez-Ullate, Dutta, Francisco Marcellán, Grandati, Grandati, Grandati, Gómez-Ullate, Gómez-Ullate, Gómez-Ullate, Gómez-Ullate, Gómez-Ullate, Gómez-Ullate, Gómez-Ullate, Gómez-Ullate, Gómez-Ullate, Gómez-Ullate, Ho, Ho, Karlin, Krall, Krall, Krein, Midya, Odake, Odake, Odake, Odake, Odake, Post, Quesne, Quesne, Quesne, Robert Milson, Routh, Sasaki, Szegő, Tanaka, Zhedanov   +44 more
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On the Darboux-Nijenhuis Variables for the Open Toda Lattice [PDF]

, 2006
We discuss two known constructions proposed by Moser and by Sklyanin of the Darboux-Nijenhuis coordinates for the open Toda lattice.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics ...
Grigoryev, Yuriy A., Tsiganov, Andrey V.
core   +4 more sources

Binary Bell polynomials and Darboux covariant Lax pairs [PDF]

Glasgow Mathematical Journal, 2001
Hirota representations of soliton equations have proved very useful. They produced many of the known families of multisoliton solutions, and have often led to a disclosure of the underlying Lax systems and infinite sets of conserved quantities. A striking feature is the ease with which direct insight can be gained into the nature of the eigenvalue ...
Lambert, Franklin, Springael, Johan, Leble, S.b.   +2 more
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A Christoffel–Darboux formula for multiple orthogonal polynomials

Journal of Approximation Theory, 2004
11 pages, no ...
Daems, E., Kuijlaars, A.B.J.
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Finding non-polynomial positive invariants and lyapunov functions for polynomial systems through Darboux polynomials [PDF]

2014 American Control Conference, 2014
In this paper, we focus on finding positive invari-ants and Lyapunov functions to establish reachability and stability properties, respectively, of polynomial ordinary differential equations (ODEs). In general, the search for such functions is a hard problem.
Goubault, Eric, Jourdan, Jacques-Henri, Putot, Sylvie, Sankaranarayanan, Sriram   +3 more
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Elementary Darboux transformations and factorization

, 2005
A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones.
A. B. Shabat, A. B. Shabat, A. P. Veselov, A. V. Domrin, F. Musso, I. T. Khabibullin, J. Hietarinta, V. E. Adler, V. E. Zakharov   +8 more
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