Results 41 to 50 of about 8,235 (175)

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.
Barrios Rolanía, Maria Dolores, García Ardila, Juan Carlos, Manrique Gamo, Daniel   +2 more
openaire   +4 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, Adrián Ruiz, Concepción Muriel   +2 more
wiley   +1 more source

Local solutions to Darboux problem with a discontinuous right-hand side

Condensed Matter Physics, 2008
The existence of a local solution to the Darboux problem uxy(x,y)=g(u(x,y)), u(x,0)=u(0,y)=0, where g is Lebesgue measurable and has at most polynomial growth, is proved.
P.Pikuta
doaj   +1 more source

Integrability of planar polynomial differential systems through linear differential equations [PDF]

, 2005
In this work, we consider rational ordinary differential equations dy/dx = Q(x,y)/P(x,y), with Q(x,y) and P(x,y) coprime polynomials with real coefficients.
Giacomini, Héctor, Giné, Jaume, Grau, Maite   +2 more
core   +6 more sources

Scattering theory for difference equations with operator coefficients

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We investigate a class of second‐order difference equations featuring operator‐valued coefficients with the aim of approaching problems of stationary scattering theory. We focus on various compact perturbations of the discrete Laplacian given in a Hilbert space of bi‐infinite square‐summable sequences with entries from a fixed Hilbert space ...
David Sher, Luis Silva, Boris Vertman, Monika Winklmeier   +3 more
wiley   +1 more source

Finite cyclicity of the contact point in slow-fast integrable systems of Darboux type

Electronic Journal of Differential Equations, 2020
Using singular perturbation theory and family blow-up we prove that nilpotent contact points in deformations of slow-fast Darboux integrable systems have finite cyclicity. The deformations are smooth or analytic depending on the region in the parameter
Renato Huzak
doaj  

Noncommutative bispectral Darboux transformations

, 2016
We prove a general theorem establishing the bispectrality of noncommutative Darboux transformations. It has a wide range of applications that establish bispectrality of such transformations for differential, difference and q-difference operators with ...
Geiger, Joel, Horozov, Emil, Yakimov, Milen   +2 more
core   +1 more source

Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras [PDF]

, 1992
Darboux coordinates are constructed on rational coadjoint orbits of the positive frequency part $\wt{\frak{g}}^+$ of loop algebras. These are given by the values of the spectral parameters at the divisors corresponding to eigenvector line bundles over ...
A. Clebsch, A.G. Reiman, B. Kostant, B.A. Dubrovin, C. Neumann, H. Flaschka, H. Knörrer, I.B. Frenkel, I.M. Gel'fand, I.M. Krichever, I.M. Krichever, J. Harnad, J. Harnad, J. Hurtubise, J. Moser, L. Gagnon, L.A. Dickey, M. Adler, M. Adler, M. R. Adams, M.R. Adams, M.R. Adams, M.R. Adams, M.R. Adams, M.R. Adams, M.R. Adams, P. Griffiths, P. Moerbeke van, R. Schilling, T. Ratiu, W. Symes   +30 more
core   +3 more sources

Convergence properties of dynamic mode decomposition for analytic interval maps

Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 179-206, February 2026.
Abstract Extended dynamic mode decomposition (EDMD) is a data‐driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method with N$N$ functions and a quadrature method with M$M$ quadrature nodes.
Elliz Akindji, Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just   +3 more
wiley   +1 more source

Exceptional Differential Polynomial Systems Formed by Simple Pseudo-Wronskians of Jacobi Polynomials and Their Infinite and Finite X-Orthogonal Reductions

Mathematics
The paper advances a new technique for constructing the exceptional differential polynomial systems (X-DPSs) and their infinite and finite orthogonal subsets.
Gregory Natanson
doaj   +1 more source