Results 41 to 50 of about 8,283 (176)

Bispectral algebras of commuting ordinary differential operators

, 1996
We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank $N$. It combines and unifies the ideas of Duistermaat-Gr\"unbaum and Wilson.
Bakalov, B., Horozov, E., Yakimov, M.
core   +3 more sources

Equivalences of the Multi-Indexed Orthogonal Polynomials [PDF]

, 2013
Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion.
Odake, Satoru
core   +3 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

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  

Spectral curve, Darboux coordinates and Hamiltonian structure of periodic dressing chains

, 2002
A chain of one-dimensional Schr\"odinger operators connected by successive Darboux transformations is called the ``Darboux chain'' or ``dressing chain''. The periodic dressing chain with period $N$ has a control parameter $\alpha$.
Adams, Adler, Burchnall, Drinfeld, Dubrovin, Dubrovin, Flaschka, Garnier, Harnad, Harnad, Kanehisa Takasaki, Krichever, Lax, McKean, Moore, Noumi, Novikov, Okamoto, Shabat, Shabat, Sklyanin, Veselov   +21 more
core   +4 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

The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2 [PDF]

Opuscula Mathematica, 2004
The structure properties of multidimensional Delsarte transmutation operators in parametric functional spaces are studied by means of differential-geometric tools.
J. Golenia, Y. A. Prykarpatsky, A. M. Samoilenko, A. K. Prykarpatsky   +3 more
doaj  

Finiteness of integrable $n$-dimensional homogeneous polynomial potentials

, 2007
We consider natural Hamiltonian systems of $n>1$ degrees of freedom with polynomial homogeneous potentials of degree $k$. We show that under a genericity assumption, for a fixed $k$, at most only a finite number of such systems is integrable.
Ablowitz, Ablowitz, Furta, Goriely, Grammaticos, Grammaticos, Guillot, Hietarinta, Hietarinta, Iwasaki, Kowalevski, Kowalevski, Kozlov, Lakshmanan, Lyapunov, Maciejewski, Maciejewski, Maciejewski, Maria Przybylska, Morales-Ruiz, Morales-Ruiz, Morales-Ruiz, Nakagawa, Nowicki, Painlevé, Ramani, Ramani, van der Put, Whittaker, Yoshida, Yoshida, Ziglin, Ziglin   +32 more
core   +2 more sources

Isospectral Flow and Liouville-Arnold Integration in Loop Algebras [PDF]

, 1993
A number of examples of Hamiltonian systems that are integrable by classical means are cast within the framework of isospectral flows in loop algebras.
A.G. Reiman, B.A. Dubrovin, C. Neumann, E. Previato, E. Previato, I.M. Krichever, J. Moser, M. Adler, M.R. Adams, M.R. Adams, M.R. Adams, M.R. Adams, MR. Adams, S.J. Al'ber   +13 more
core   +2 more sources