Results 41 to 50 of about 1,141,931 (185)
Isotopy and equivalence of knots in 3‐manifolds
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract Two knots K$K$ and J$J$ in S3$S^3$ are isotopic if and only if they are related by an orientation‐preserving diffeomorphism of S3$S^3$. This claim follows from the fact that any orientation‐preserving self‐diffeomorphism of S3$S^3$ is isotopic to the identity. We show that this same idea applies to any prime oriented closed 3‐manifold.
Paolo Aceto +4 more
wiley +1 more source
MathematicsDarboux 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
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Integrable Abelian vortex-like solitons
Physics Letters B, 2017 We propose a modified version of the Ginzburg–Landau energy functional admitting static solitons and determine all the Painlevé-integrable cases of its Bogomolny equations of a given class of models.
Felipe Contatto
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Littlewood, Paley and almost‐orthogonality: a theory well ahead of its time
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract The classic paper by Littlewood and Paley [J. Lond. Math. Soc. (1), 6 (1931), 230–233] marked the birth of Littlewood–Paley theory. We discuss this paper and its impact from a historical perspective, include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them ...
Anthony Carbery
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Noncommutative polygonal cluster algebras
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein–Retakh, and are inspired by the emerging theory of Θ$\Theta$‐positivity for the groups Spin(p,q)$\mathrm{Spin}(p,q)$.
Zachary Greenberg +3 more
wiley +1 more source
Singularity Analysis and Integrability of a Burgers-Type System of Foursov
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We apply the Painlevé test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess infinitely many commuting local generalized symmetries ...
Sergei Sakovich
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Sublinear bilipschitz equivalence and the quasiisometric classification of solvable Lie groups
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner, and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families of solvable groups which share the same dimension, cone‐dimension and Dehn function ...
Ido Grayevsky, Gabriel Pallier
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The Painlevé Equations and Discrete Asymptotics
, 2017 Littlewood reported in his preface to Hardy’s "Divergent Series” that Abel said divergent series were the invention of the devil. But such series arise commonly in the solutions of ODEs in asymptotic limits.
Joshi, Nalini
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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
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Deformation of Okamoto–Painlevé pairs and Painlevé equations
, 2001 In this paper, we introduce the notion of a generalized rational Okamoto–Painlevé pair ( S , Y ) (S, Y) by generalizing the notion of the spaces of initial conditions of Painlevé equations.
Taro Takebe +2 more
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