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Exceptional orthogonal polynomials and the Darboux transformation [PDF]
Journal of Physics A: Mathematical and Theoretical, 2010 We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described $X_m$ Laguerre polynomials in terms of an isospectral Darboux transformation.
Atkinson F V +21 more
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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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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
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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
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Darboux Integrability of a Generalized 3D Chaotic Sprott ET9 System
مجلة بغداد للعلوم, 2022 In this paper, the first integrals of Darboux type of the generalized Sprott ET9 chaotic system will be studied. This study showed that the system has no polynomial, rational, analytic and Darboux first integrals for any value of .
Adnan Ali Jalal +2 more
doaj +1 more source
Darboux integrability of a hyperjerk memristive system
Zanco Journal of Pure and Applied Sciences, 2023 In this work, we investigate the following novel four-dimensional dynamical memristive system (see, (Prousalis et al., 2017)) This system, in a certain area of the parameter space, exhibits hyper-jerk dynamics and a line of singularities passing ...
Niazy Hady Hussein ,Soran Mohammed Khudur
doaj +1 more source
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 and rational first integrals for a family of cubic three dimensional systems
Zanco Journal of Pure and Applied Sciences, 2021 In this paper, we investigate the first integrals of the following system exam.PNG exam1.PNG This kind of system is a particular case of the jerk cubic three dimensional polynomial differential systems.
Sarbast Hussein Mikaeel, Azad I. Amen
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On generalized Heun equation with some mathematical properties
Acta Polytechnica, 2022 We study the analytic solutions of the generalized Heun equation, (α0 + α1 r + α2 r2 + α3 r3) y′′ + (β0 + β1 r + β2 r2) y′ + (ε0 + ε1 r) y = 0, where |α3| + |β2|≠ 0, and {αi}3i=0, {βi}2i=0, {εi}1i=0 are real parameters.
Nasser Saad
doaj +1 more source
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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