Results 51 to 60 of about 8,283 (176)

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 Askey–Wilson-type polynomials through Darboux–Crum transformations [PDF]

Journal of Physics A: Mathematical and Theoretical, 2010
An alternative derivation is presented of the infinitely many exceptional Wilson and Askey-Wilson polynomials, which were introduced by the present authors in 2009. Darboux-Crum transformations intertwining the discrete quantum mechanical systems of the original and the exceptional polynomials play an important role.
Odake, Satoru, Sasaki, Ryu
openaire   +2 more sources

Large‐Amplitude Periodic Solutions to the Steady Euler Equations With Piecewise Constant Vorticity

Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.
ABSTRACT We consider steady solutions to the incompressible Euler equations in a two‐dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation theory, we rigorously construct curves of solutions that terminate either with stagnation on the interface ...
Alex Doak, Karsten Matthies, Jonathan Sewell, Miles H. Wheeler   +3 more
wiley   +1 more source

Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations [PDF]

Journal of Sciences, Islamic Republic of Iran, 2006
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i.
doaj  

Bright and Dark Breathers on an Elliptic Wave in the Defocusing mKdV Equation

Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.
ABSTRACT Breathers on an elliptic wave background consist of nonlinear superpositions of a soliton and a periodic wave, both traveling with different wave speeds and interacting periodically in the space‐time. For the defocusing modified Korteweg–de Vries equation, the construction of general breathers has been an open problem since the elliptic wave ...
Dmitry E. Pelinovsky, Rudi Weikard
wiley   +1 more source

On Finite Exceptional Orthogonal Polynomial Sequences Composed of Rational Darboux Transforms of Romanovski-Jacobi Polynomials

Axioms
The paper presents the united analysis of the finite exceptional orthogonal polynomial (EOP) sequences composed of rational Darboux transforms of Romanovski-Jacobi polynomials.
Gregory Natanson
doaj   +1 more source

Askey-Wilson Type Functions, With Bound States

, 2003
The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful ...
A. Kasman, A.S. Zhedanov, B. Bakalov, B. Bakalov, D. Mumford, E. Koelink, F.A. Grünbaum, F.A. Grünbaum, F.A. Grünbaum, F.A. Grünbaum, F.W. Nijhoff, G. Andrews, G. Segal, G. Wilson, G. Wilson, H.L. Krall, I. Cherednik, J. Koekoek, J.J. Duistermaat, L. Haine, L. Haine, L. Haine, L.L. Littlejohn, Luc Haine, M. Rahman, M. Rahman, M. Toda, M.E.H. Ismail, P. Iliev, P. Iliev, Plamen Iliev, S. Bochner, S.K. Suslov, S.K. Suslov, T.H. Koornwinder, V.P. Spiridonov, W.N. Everitt   +36 more
core   +1 more source

Dynamical Behavior and Chaotic Nature of M‐Fractional Paraxial Wave Equation With Three Analytical Methods

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
This research work provides a comprehensive investigation of the M‐fractional paraxial wave equation (M‐fPWE) in describing complex optical phenomena in telecommunication systems and nonlinear media, focusing on the dynamical analysis of optical soliton solutions, the impact of M‐fractional parameters, stability, multistability, and the chaotic nature ...
Md. Mamunur Roshid, Mahtab Uddin, Mohammad Safi Ullah, Golam Mostafa, Ashek Ahmed, Shikha Binwal   +5 more
wiley   +1 more source

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

Polynomial and rational integrability of polynomial Hamiltonian systems

Electronic Journal of Differential Equations, 2012
Within the class of canonical polynomial Hamiltonian systems anti-symmetric under phase-space involutions, we generalize some results on the existence of Darboux polynomial and rational first integrals for "kinetic plus potential" systems to general ...
Jaume Llibre, Cristina Stoica, Claudia Valls   +2 more
doaj