Results 21 to 30 of about 187 (156)
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. We also show that the shape-invariance of these new polynomial families is a direct consequence of the ...
Gómez-Ullate Otaiza, David +2 more
openaire +4 more sources
Dual Szegö pairs of sequences of rational matrix-valued functions
International Journal of Mathematics and Mathematical Sciences, 2006 We study certain sequences of rational matrix-valued functions with poles outside the unit circle. These sequences are recursively constructed based on a sequence of complex numbers with norm less than one and a sequence of strictly contractive matrices.
Andreas Lasarow
doaj +1 more source
Darboux transformation of symmetric Jacobi matrices and Toda lattices
Frontiers in Applied Mathematics and StatisticsLet J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively.
Ivan Kovalyov, Oleksandra Levina
doaj +1 more source
MathematicsDarboux transformations are relations between the eigenfunctions and coefficients of a pair of linear differential operators, while Painlevé equations are nonlinear ordinary differential equations whose solutions arise in diverse areas of applied ...
Joe W. E. Harrow, Andrew N. W. Hone
doaj +1 more source
On algebraic integrals of a differential equation
Discrete and Continuous Models and Applied Computational Science, 2019 We consider the problem of integrating a given differential equation in algebraic functions, which arose together with the integral calculus, but still is not completely resolved in finite form.
Mikhail D Malykh +2 more
doaj +1 more source
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
openaire +2 more sources
Christoffel–Darboux Type Identities for the Independence Polynomial [PDF]
Combinatorics, Probability and Computing, 2018 In this paper we introduce some Christoffel–Darboux type identities for independence polynomials. As an application, we give a new proof of a theorem of Chudnovsky and Seymour, which states that the independence polynomial of a claw-free graph has only real roots. Another application is related to a conjecture of Merrifield and Simmons.
openaire +2 more sources
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 4, April 2026.ABSTRACT The Lie group SE3$SE\left(3\right)$ of isometric orientation‐preserving transformation is used for modeling multibody systems, robots, and Cosserat continua. The use of these models in numerical simulation and optimization schemes necessitates the exponential map, its right‐trivialized differential (often referred to as the tangent operator ...
Andreas Müller
wiley +1 more source
Automated Reasoning For The Existence Of Darboux Polynomials
Proceedings of the 2024 International Symposium on Symbolic and Algebraic ComputationGiven a polynomial ordinary differential equation (ODE), we devise generic polynomial reduction algorithms to automatically investigate the intertwined relationship between the total degree of (nontrivial) Darboux polynomials and the polynomials defining the ODE.
Ghorbal, Khalil, Bridoux, Maxime
openaire +2 more sources
C∞‐Structures for Liénard Equations and New Exact Solutions to a Class of Klein–Gordon Equations
Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2795-2822, 15 March 2026.ABSTRACT Liénard equations are analyzed using the recent theory of 𝒞∞‐structures. For each Liénard equation, a 𝒞∞‐structure is determined by using a Lie point symmetry and a 𝒞∞‐symmetry. Based on this approach, a novel method for integrating these equations is proposed, which consists in solving sequentially two completely integrable Pfaffian equations.
Beltrán de la Flor +2 more
wiley +1 more source