Results 51 to 60 of about 6,848 (171)

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

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

Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts [PDF]

, 2017
In our previous papers, the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials and the Casoratian identities for the Askey-Wilson polynomial and its reduced form polynomials were presented.
Odake, Satoru
core   +3 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

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

The role of algebraic solutions in planar polynomial differential systems [PDF]

, 2005
We study a planar polynomial differential system, given by \dot{x}=P(x,y), \dot{y}=Q(x,y). We consider a function I(x,y)=\exp \{h_2(x) A_1(x,y) \diagup A_0(x,y) \} h_1(x) \prod_{i=1}^{\ell} (y-g_i(x))^{\alpha_i}, where g_i(x) are algebraic functions, A_1(
Giacomini, Héctor, Giné, Jaume, Grau, Maite   +2 more
core   +5 more sources

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

Darboux Integrability Of the Biological System

Al-Rafidain Journal of Computer Sciences and Mathematics
In the given paper, we investigate the integrability of a mathematical model of a 3D biological system. Our results show that the system admits a polynomial first integrals for some parameters, an invariant algebraic surface with an exponential factor ...
Zakariya Hashem Ali, Ahmad Muhamad Husien   +1 more
doaj   +1 more source

Cauchy Biorthogonal Polynomials

, 2009
The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positive kernel and a pair of positive measures on the positive axis we define ...
Aptekarev, Aptekarev, Beals, Beals, Bertola, Bertola, Bertola, Bertola, Bertola, Bertola, Camassa, Cryer, Cryer, Degasperis, Duits, Ercolani, Eynard, Fidalgo Prieto, Gantmacher, J. Szmigielski, Jimbo, Karlin, Kuijlaars, Lundmark, Lundmark, M. Bertola, M. Gekhtman, Mehta, Nikishin, Nikišin, Sorokin, Sorokin, Sorokin, Van Assche   +33 more
core   +2 more sources

Exploring the Chavy–Waddy–Kolokolnikov Model: Analytical Study via Recently Developed Techniques

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This work explores the analytical soliton solutions to the Chavy–Waddy–Kolokolnikov equation (CWKE), which is a well‐known equation in biology that shows how light‐attracted bacteria move together. This equation is very useful for analyzing pattern creation, instability regimes, and minor changes in linear situations since bacterial movement is very ...
Jan Muhammad, David Yaro, Usman Younas, Chang Phang   +3 more
wiley   +1 more source