Results 41 to 50 of about 6,848 (171)

Krein-Adler transformations for shape-invariant potentials and pseudo virtual states [PDF]

, 2013
For eleven examples of one-dimensional quantum mechanics with shape-invariant potentials, the Darboux-Crum transformations in terms of multiple pseudo virtual state wavefunctions are shown to be equivalent to Krein-Adler transformations deleting multiple
Odake, Satoru, Sasaki, Ryu
core   +2 more sources

Confluent Darboux Transformations and Wronskians for Algebraic Solutions of the Painlevé III (D₇) Equation

Mathematics
Darboux 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

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

Discrete Darboux transformation for discrete polynomials of hypergeometric type

, 1998
Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn)
, Askey R, Darboux G, Gaspard Bangerezako, Kalnins E G, Magnus A P, Magnus A P, Miller W Jr, Nikiforov A, Shabat A, Shabat A B, Smirnov Yu F, Spiridonov V, Spiridonov V, Spiridonov V   +14 more
core   +1 more source

A new family of shape invariantly deformed Darboux-P\"oschl-Teller potentials with continuous \ell [PDF]

, 2010
We present a new family of shape invariant potentials which could be called a ``continuous \ell version" of the potentials corresponding to the exceptional (X_{\ell}) J1 Jacobi polynomials constructed recently by the present authors.
Andrews G E, Darboux G, Darboux G, Gendenshtein L E, Gómez-Ullate D, Ho C-L Odake S Sasaki R, Odake S, Quesne C, Quesne C, R Sasaki, S Odake, Sasaki R, Szegö G   +12 more
core   +3 more sources

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

Extensions of solvable potentials with finitely many discrete eigenstates [PDF]

, 2013
We address the problem of rational extensions of six examples of shape-invariant potentials having finitely many discrete eigenstates. The overshoot eigenfunctions are proposed as candidates unique in this group for the virtual state wavefunctions, which
Odake, Satoru, Sasaki, Ryu
core   +2 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

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

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