Results 81 to 90 of about 1,020 (214)

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source

Zeros of the Wronskian of a polynomial

Journal of Mathematical Analysis and Applications, 1991
The authors study the zeros of the polynomials \(p\) and \(W(p,p')\), where \(W(p,p')=pp''-p'{}^ 2\) (Wronskian of \(p,p'\)). A sample result: If \(d\) is the minimum distance between two consecutive zeros of \(p\), then the imaginary part of the zeros of \(W(p,p')\) cannot be less than \(\sqrt 3 d/4\).
Dilcher, Karl, Stolarsk, Kenneth B
openaire   +1 more source

Principal frequency of clamped plates on RCD(0,N)${\sf RCD}(0,N)$ spaces: Sharpness, rigidity, and stability

Proceedings of the London Mathematical Society, Volume 131, Issue 2, August 2025.
Abstract We study fine properties of the principal frequency of clamped plates in the (possibly singular) setting of metric measure spaces verifying the RCD(0,N)${\sf RCD}(0,N)$ condition, that is, infinitesimally Hilbertian spaces with nonnegative Ricci curvature and dimension bounded above by N>1$N>1$ in the synthetic sense.
Alexandru Kristály, Andrea Mondino
wiley   +1 more source

Existence and Orbital Stability of Standing‐Wave Solutions of the Nonlinear Logarithmic Schrödinger Equation On a Tadpole Graph

Studies in Applied Mathematics, Volume 155, Issue 1, July 2025.
ABSTRACT This work aims to study some dynamical aspects of the nonlinear logarithmic Schrödinger equation (NLS‐log) on a tadpole graph, namely, a graph consisting of a circle with a half‐line attached at a single vertex. By considering Neumann–Kirchhoff boundary conditions at the junction, we show the existence and the orbital stability of standing ...
Jaime Angulo Pava, Andrés Gerardo Pérez Yépez   +1 more
wiley   +1 more source

Wronskian and Gram Solutions to Integrable Equations using Bilinear Methods [PDF]

, 2017
This thesis presents Wronskian and Gram solutions to both the Korteweg-de Vries and Kadomtsev-Petviashvili equations, which are then scalable to arbitrarily large numbers of interacting solitons.
Wiggins, Benjamin
core  

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

Maximal cuts in arbitrary dimension

Journal of High Energy Physics, 2017
We develop a systematic procedure for computing maximal unitarity cuts of multiloop Feynman integrals in arbitrary dimension. Our approach is based on the Baikov representation in which the structure of the cuts is particularly simple. We examine several
Jorrit Bosma, Mads Sogaard, Yang Zhang
doaj   +1 more source

On Asymptotic Behaviors of Acoustic Waves Due to High‐Contrast Material Inclusions

Studies in Applied Mathematics, Volume 154, Issue 4, April 2025.
ABSTRACT This paper investigates the asymptotic behaviors of time‐harmonic acoustic waves generated by an incident wave illuminating inhomogeneous medium inclusions with high‐contrast material parameters. We derive sharp asymptotic estimates and obtain several effective acoustic obstacle scattering models when the material parameters take extreme ...
Yueguang Hu, Hongyu Liu
wiley   +1 more source

Applications of the Wronskian and Gram matrices of {tieλkt} [PDF]

, 1982
A review is made of some of the fundamental properties of the sequence of functions {tieλkt}, k = 1,…,s, i = 0,…,mk−1, distinct λ i. In particular it is shown how the Wronskian and Gram matrices of this sequence of functions appear naturally in such ...
Hartwig, Robert E.
core   +1 more source

q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy

Symmetry, Integrability and Geometry: Methods and Applications, 2006
Using the determinant representation of gauge transformation operator, we have shown that the general form of $au$ function of the $q$-KP hierarchy is a $q$-deformed generalized Wronskian, which includes the $q$-deformed Wronskian as a special case.
Jingsong He, Yinghua Li, Yi Cheng
doaj