Results 11 to 20 of about 8,283 (176)
Seeking Darboux Polynomials [PDF]
Acta Applicandae Mathematicae, 2014 We introduce several techniques which allow to simplify the expression of the cofactor of Darboux polynomials of polynomial differential systems in R^n. We apply these techniques to some well-known systems when n = 2, 3, 4. We also propose a general method for computing Darboux polynomials in the plane.
Ferragut, Antoni +1 more
exaly +8 more sources
Liouvillian Integrability Versus Darboux Polynomials [PDF]
Qualitative Theory of Dynamical Systems, 2016 Agraïments: FEDER/UNAB10-4E-378. The second author is supported by Portuguese National Funds through FCT - Fundacâo para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD. The third author is partially supported by NNSF of China grant number 11271252, by RFDP of Higher Education of China grant number 20110073110054, and by ...
Llibre, Jaume +2 more
exaly +8 more sources
Darboux polynomials and first integrals of natural polynomial Hamiltonian systems [PDF]
Physics Letters A, 2004 We show that for a natural polynomial Hamiltonian system the existence of a single Darboux polynomial (a partial polynomial first integral) is equivalent to the existence of an additional first integral functionally independent with the Hamiltonian function.
Maciejewski, Andrzej J. +1 more
exaly +5 more sources
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 Integrability of Polynomial Differential Systems [PDF]
Qualitative Theory of Dynamical Systems, 2011 A method to find explicit closed forms for a first integral of a planar polynomial differential system from its invariant algebraic curves was given by \textit{G. Darboux} [C. R. LXXXVI, 581--586 (1878; JFM 10.0214.03)]. From that moment on, many research articles were devoted to the study of the integrability problem by using the invariant algebraic ...
Llibre, Jaume, Zhang, Xiang
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Exceptional Legendre Polynomials and Confluent Darboux Transformations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial sequences that miss a finite number of ''exceptional'' degrees.
Garcia Ferrero, María Ángeles +2 more
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Dual optimal design and the Christoffel–Darboux polynomial [PDF]
Optimization Letters, 2021 The purpose of this short note is to show that the Christoffel-Darboux polynomial, useful in approximation theory and data science, arises naturally when deriving the dual to the problem of semi-algebraic D-optimal experimental design in statistics. It uses only elementary notions of convex analysis.
de Castro, Yohann +3 more
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Darboux Polynomials for Lotka–Volterra Systems in Three Dimensions [PDF]
Journal of Nonlinear Mathematical Physics, 2021 We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors.
Christodoulides, Y. T. +3 more
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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials [PDF]
, 2013 We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic ...
Gomez-Ullate, David +2 more
core +4 more sources
Derivations of polynomial algebras without Darboux polynomials
Journal of Pure and Applied Algebra, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ollagnier, Jean Moulin, Nowicki, Andrzej
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