Results 121 to 130 of about 187 (156)
DARBOUX TRANSFORMS AND ORTHOGONAL POLYNOMIALS [PDF]
Bulletin of the Korean Mathematical Society, 2002 In [\textit{F. A. Grünbaum} and \textit{L. Haine}, Symmetries and Integrability of Differential Equations, Estérel, 1994, CRM Proc. Lect. Notes 9, 143-154 (1996; Zbl 0865.33008)] the Darboux transform was used to obtain so-called Bochner-Krall orthogonal polynomials which satisfy a higher order (\(>2\)) spectral type differential equation. This Darboux
Gang-Joon Yoon
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On the Darboux transformations and sequences of p-orthogonal polynomials [PDF]
Applied Mathematics and Computation, 2020 For a fixed $p \in \mathbb{N}$, sequences of polynomials $\{P_n\}$, $n \in \mathbb{N}$, defined by a $(p+2)$-term recurrence relation are related to several topics in Approximation Theory. A $(p+2)$-banded matrix $J$ determines the coefficients of the recurrence relation of any of such sequences of polynomials.
D Barrios Rolanía +2 more
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Darboux polynomials and first integrals of polynomial Hamiltonian systems
Communications in Nonlinear Science and Numerical Simulation, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrei Pranevich +2 more
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On the Christoffel–Darboux formula for generalized matrix orthogonal polynomials
Journal of Mathematical Analysis and Applications, 2014 We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal ...
Manuel Mañas
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A Christoffel–Darboux formula for multiple orthogonal polynomials
Journal of Approximation Theory, 2004 11 pages, no ...
Evi Daems, Arno B. J. Kuijlaars
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Darboux Polynomials for Lie Algebras
IFAC Proceedings Volumes, 2011Abstract Darboux polynomials and relative characteristic polynomials extend to time-invariant nonlinear systems the concept of eigenvector-eigenvalue pair for linear systems, and are, therefore, very useful to depict the behavior of the system. In this article, using tools such as Lie algebras, it is shown how Darboux polynomials can be characterized ...
MENINI, LAURA, TORNAMBE', ANTONIO
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The Darboux Polynomials and Integrability of Polynomial Levinson–Smith Differential Equations
International Journal of Bifurcation and Chaos, 2023We provide the necessary and sufficient conditions of Liouvillian integrability for nondegenerate near infinity polynomial Levinson–Smith differential equations. These equations generalize Liénard equations and are used to describe self-sustained oscillations. Our results are valid for arbitrary degrees of the polynomials arising in the equations.
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Journal of Complexity, 2011 In this paper we study planar polynomial differential systems of this form: dX/dt=A(X, Y), dY/dt= B(X, Y), where A,B belongs to Z[X, Y], degA \leq d, degB \leq d, and the height of A and B is smaller than H. A lot of properties of planar polynomial differential systems are related to irreducible Darboux polynomials of the corresponding derivation: D =A(
Guillaume Chèze
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Homogeneous darboux polynomials and generalising integrable ODE systems
Journal of Computational Dynamics, 2021 This is a pre-copy-editing, author-produced PDF of an article accepted for publication in [insert journal title] following peer review. The definitive publisher-authenticated version [insert complete citation information here] is available online at: http://www.aimsciences.org/article/doi/10.3934/jcd.2021001 We show that any system of ODEs can be ...
van der Kamp, Peter H. +2 more
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DARBOUX POLYNOMIALS AND ALGEBRAIC INTEGRABILITY OF THE CHEN SYSTEM
International Journal of Bifurcation and Chaos, 2007In this paper, we characterize all the Darboux polynomials of the Chen system, [Formula: see text], and prove that the system is not algebraic integrability. For proving the results, we use the weight homogeneous polynomials and the method of characteristics.
Tinghua Lü, Xiang Zhang
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