Results 51 to 60 of about 1,222,314 (174)

Nonlocal Symmetry, CRE Solvability, and Exact Interaction Solutions of the (2 + 1)-Dimensional Boussinesq Equation

Journal of Mathematics, 2022
The (2 + 1)-dimensional Boussinesq equation is considered in this study. Nonlocal symmetries of the (2 + 1)-dimensional Boussinesq equation are obtained by means of the truncated Painlevé expansion.
Sixing Tao
doaj   +1 more source

Counting problems for orthogonal sets and sublattices in function fields

Mathematika, Volume 72, Issue 2, April 2026.
Abstract Let K=Fq((x−1))$\mathcal {K}=\mathbb {F}_q((x^{-1}))$. Analogous to orthogonality in the Euclidean space Rn$\mathbb {R}^n$, there exists a well‐studied notion of ultrametric orthogonality in Kn$\mathcal {K}^n$. In this paper, we extend the work of [4] on counting problems related to orthogonality in Kn$\mathcal {K}^n$.
Noy Soffer Aranov, Angelot Behajaina
wiley   +1 more source

The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I

Symmetry, Integrability and Geometry: Methods and Applications, 2011
We wish to explore a link between the Lax integrability of the q-Painlevé equations and the symmetries of the q-Painlevé equations. We shall demonstrate that the connection preserving deformations that give rise to the q-Painlevé equations may be thought
Christopher M. Ormerod
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

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

Irregular conformal blocks, Painlevé III and the blow-up equations

Journal of High Energy Physics, 2020
We study the relation of irregular conformal blocks with the Painlevé III3 equation. The functional representation for the quasiclassical irregular block is shown to be consistent with the BPZ equations of conformal field theory and the Hamilton-Jacobi ...
Pavlo Gavrylenko, Andrei Marshakov, Artem Stoyan   +2 more
doaj   +1 more source

Joint distribution of Hecke eigenforms on H3$ \mathbb {H}^3$

Mathematische Nachrichten, Volume 299, Issue 3, Page 661-674, March 2026.
Abstract We prove a joint value equidistribution statement for Hecke–Maaß cusp forms on the hyperbolic three‐space H3$\mathbb {H}^3$. This supports the conjectural statistical independence of orthogonal cusp forms.
Didier Lesesvre, Luca Marchesini, Nicole Raulf   +2 more
wiley   +1 more source

Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them

Symmetry, Integrability and Geometry: Methods and Applications, 2010
We study the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. Divisibility properties of the coefficients of these polynomials, concerning powers of 4, are obtained and ...
Pieter Roffelsen
doaj   +1 more source

Model pluralism for logic

Noûs, Volume 60, Issue 1, Page 136-160, March 2026.
Abstract It is well‐recognized in the sciences that a multitude of nonequivalent models are used by researchers to fulfill a range of goals, even for the same target system, a result known broadly as model pluralism. The possibility of the same form of pluralism occurring in logic, however, has not been adequately considered.
Ben Martin
wiley   +1 more source

Series and Rational Solutions of the Second Kind Painlevé Equations by Using the Quantum Pseudospectral Method

International Journal of Mathematics and Mathematical Sciences
The Painlevé equations and their series and rational solutions are essential in applied, pure mathematics and theoretical physics. Recently, quantum algorithms have helped to implement numerical algorithms more easily by performing linear algebra in our ...
Saeid Abbasbandy
doaj   +1 more source