On the relation between Darboux transformations and polynomial mappings
Journal of Approximation Theory, 2013 Let dμ(t) be a probability measure on [0,+\infty) such that its moments are finite. Then the Cauchy-Stieltjes transform S of dμ(t) is a Stieltjes function, which admits an expansion into a Stieltjes continued fraction. In the present paper, we consider a matrix interpretation of the unwrapping transformation from S(λ) to λS(λ^2), which is intimately ...
openaire +3 more sources
Darboux transformations for multivariate orthogonal polynomials
, 2015 In this version we have not only added two more bibliographic references but also performed major changes in Section 3 on poised sets. This was motivated by our recent finding that full column rank of the Vandermonde matrix is not only necessary but sufficient.
Ariznabarreta, Gerardo, Mañas, Manuel
openaire +2 more sources
On Computation of Darboux Polynomials for Full Toda Lattice
Communications in Nonlinear Science and Numerical SimulationOne of the oldest methods for computing invariants of ordinary differential equations is tested using the full Toda lattice model. We show that the standard method of undetermined coefficients and modern symbolic algebra tools together with sufficient computing power allow to compute Darboux invariants without any additional information.
openaire +3 more sources
Factorization of Dual Quaternion Polynomials Without Study's Condition. [PDF]
Adv Appl Clifford Algebr, 2021 Siegele J, Pfurner M, Schröcker HP.
europepmc +1 more source
Derivations on Polynomial Rings and the Darboux Polynomials [PDF]
Revista Ciencias Exatas e Naturais, 2017 Wálmisson Régis de Almeida +1 more
openaire +1 more source
Efficient Nyström-type method for the solution of highly oscillatory Volterra integral equations of the second kind. [PDF]
PLoS One, 2023 Wu Q, Sun M.
europepmc +1 more source
Coexistence of chaotic attractor and unstable limit cycles in a 3D dynamical system. [PDF]
Open Res Eur, 2021 Constantinescu D, Tigan G, Zhang X.
europepmc +1 more source
Darboux transforms on Band Matrices, Weights and associated Polynomials
, 2000 Classically, it is well known that a single weight on a real interval leads to orthogonal polynomials. In "Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems", Comm. Math. Phys. 207, pp. 589-620 (1999), we have shown that $m$-periodic sequences of weights lead to "moments", polynomials defined by determinants of matrices ...
Adler, Mark, van Moerbeke, Pierre
openaire +3 more sources
Simple Darboux points of polynomial planar vector fields
Journal of Pure and Applied Algebra, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions. [PDF]
Heliyon, 2023 Guo B, Fang Y, Dong H.
europepmc +1 more source