Results 81 to 90 of about 45,379 (233)

Riemann-Hilbert approach for the integrable nonlocal nonlinear Schr\"odinger equation with step-like initial data

Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2018
We study the Cauchy problem for the integrable nonlocal nonlinear Schr\"odinger (NNLS) equation \[ iq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0 \] with a step-like initial data: $q(x,0)=o(1)$ as $x\to-\infty$ and $q(x,0)=A+o(1)$ as $x\to\infty ...
Ya. Rybalko, D. G. Shepelsky
doaj  

Crack Propagation in the Human Bone. Mode I of Fracture

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
The problem of crack propagation in human bone is studied. We for- mulate and solve the mathematical problem for the pre-stressed crack in Mode I of classical fracture.
Craciun E. M., Rabaea A., Popa M. F., Mihailov C. I.   +3 more
doaj   +1 more source

Riemann Hilbert problem for bi-orthogonal polynomials [PDF]

Journal of Physics A: Mathematical and General, 2003
Two sequences of polynomials which are orthogonal to each other with respect to a two-dimensional measure are called bi-orthogonal polynomials \[ \int_R \int_R P_n(\lambda)Q_m(\xi) \,d\mu(\lambda,\xi) =\delta_{mn}. \] If the measure is given by \(d\mu(\lambda,\xi) =\exp(-V(\lambda)-W(\xi)+\lambda\xi)\,d\lambda \,d\xi\), then \(V(\lambda),W(\xi)\) are ...
openaire   +1 more source

A Re‐Examination of Foundational Elements of Cosmology

Fortschritte der Physik, Volume 74, Issue 3, March 2026.
ABSTRACT This paper undertakes a conceptual re‐examination of several foundational elements of cosmology through the lens of spacetime symmetries. A new derivation of the Friedmann–Lemaître–Robertson–Walker metric is obtained by a careful conceptual examination of rotations and translations on generic manifolds, followed by solving the rotational and ...
Lavinia Heisenberg
wiley   +1 more source

Hyperderivatives of the deformation series associated with arithmetic gamma values and characteristic p$p$ multiple zeta values

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Number theory for positive characteristic contains analogues of the special values that were introduced by Carlitz; these include the Carlitz gamma values and Carlitz zeta values. These values were further developed to the arithmetic gamma values and multiple zeta values by Goss and Thakur, respectively.
Ryotaro Harada, Daichi Matsuzuki
wiley   +1 more source

Building multi-BTZ black holes through Riemann-Hilbert problem

Journal of High Energy Physics
We construct a recently found class of non-BPS black hole solutions with asymptotically AdS 3 × S 3 × T 4 in type IIB supergravity, consisting of multiple BTZ black holes localized on an S 3, within the group theoretical framework of Breitenlohner and ...
Jun-ichi Sakamoto, Shinya Tomizawa
doaj   +1 more source

Unitary ensembles with a critical edge point, their multiplicative statistics, and the Korteweg‐de‐Vries hierarchy

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We study the multiplicative statistics associated to the limiting determinantal point process describing eigenvalues of unitary random matrices with a critical edge point, where the limiting eigenvalue density vanishes like a power 5/2. We prove that these statistics are governed by the first three equations of the Korteweg‐de‐Vries (KdV ...
Mattia Cafasso, Carla Mariana da Silva Pinheiro   +1 more
wiley   +1 more source

Discrete analogues of second‐order Riesz transforms

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Discrete analogues of classical operators in harmonic analysis have been widely studied, revealing deep connections with areas such as ergodic theory and analytic number theory. This line of research is commonly known as Discrete Analogues in Harmonic Analysis (DAHA).
Rodrigo Bañuelos, Daesung Kim
wiley   +1 more source

Genus two KdV soliton gases and their long-time asymptotics

Forum of Mathematics, Sigma
This paper employs the Riemann-Hilbert problem and nonlinear steepest descent method of Deift-Zhou to provide a comprehensive analysis of the asymptotic behavior of the genus two Korteweg-de Vries soliton gases.
Deng-Shan Wang, Dinghao Zhu, Xiaodong Zhu   +2 more
doaj   +1 more source

Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann Kernel

Kurdistan Journal of Applied Research, 2017
A Robin problem is a mixed problem with a linear combination of Dirichlet and Neumann D-N conditions. The aim of this paper are presents a new boundary integral equation BIE method for the solution of unbounded Robin boundary value problem BVP in the ...
Shwan H. H. Al-Shatri, Karzan Wakil, Munira Ismail   +2 more
doaj   +1 more source