Results 31 to 40 of about 26,863 (194)

General soliton matrices in the Riemann–Hilbert problem for integrable nonlinear equations [PDF]

Journal of Mathematical Physics, 2003
We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann–Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial ...
Shchesnovich, V. S., Yang, J. K.
openaire   +4 more sources

Evaluation of the E‐polarization focusing ability in Thz range for microsize cylindrical parabolic reflector made of thin dielectric layer sandwiched between graphene

IET Microwaves, Antennas & Propagation, 2021
We consider two‐dimensional (2‐D) thin dielectric parabolic reflector, covered with graphene from both sides, illuminated symmetrically by an E‐polarized electromagnetic plane wave.
Taner Oğuzer, Ayhan Altıntaş
doaj   +1 more source

A general framework for solving Riemann–Hilbert problems numerically [PDF]

Numerische Mathematik, 2012
Let \(\Gamma\subset{\mathbb C}\) be a given contour. The author finds approximations for a function \(\Phi: {\mathbb C}\setminus\Gamma \mapsto {\mathbb C}^{2\times 2}\) which is analytic everywhere except on \(\Gamma\) such that \[ \Phi^{+}(t)=\Phi^{-}(t)G(t), \quad t\in\Gamma, \tag{RH} \] and \(\Phi(\infty) =I.\) Here \(G(t)\) is given \(2\times 2 ...
openaire   +1 more source

On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials [PDF]

, 2017
In this paper, we compute the probability that an N x N matrix from the generalized Gaussian Unitary Ensemble (gGUE) is positive definite, extending a previous result of Dean and Majumdar (2008). For this purpose, we work out the large degree asymptotics
Aazami, Anderson, Ben Arous, Bhargava, Bleher, Bleher, Boelen, Borot, Borot, Cavagna, Chihara, Clarkson, Dean, Deift, Deo, Filipuk, Fokas, Forrester, Forrester, Fyodorov, Ismail, Krasovsky, Mehta, Mehta, Pastur, Saff, Vanlessen, Witte, Zhao, Álvarez   +29 more
core   +4 more sources

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

Tau functions and the limit of block Toeplitz determinants [PDF]

, 2014
A classical way to introduce tau functions for integrable hierarchies of solitonic equations is by means of the Sato-Segal-Wilson infinite-dimensional Grassmannian.
Cafasso, Mattia, Wu, Chao-Zhong
core   +5 more sources

Anti-plane crack in human bone. I. Mathematical modelling

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
We consider an anti-plane crack in a bone, considered as an initially deformed orthotropic, linear elastic composite material. Elastic incremental fields in the composite material are obtained following theories of Guz’s representation and of Riemann ...
Crăciun Eduard Marius, Marin Marin, Răbâea Adrian   +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

Reductions of integrable equations on A.III-type symmetric spaces [PDF]

, 2010
We study a class of integrable non-linear differential equations related to the A.III-type symmetric spaces. These spaces are realized as factor groups of the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to this symmetric space
A V Mikhailov, Helgasson S, Lombardo S Sanders J, Mikhailov A, Mikhailov A V, Mikhailov A V, T I Valchev, V S Gerdjikov   +7 more
core   +1 more source

The N-soliton solutions of the n-component generalized Sasa-Satsuma system: Riemann-Hilbert method

Nuclear Physics B
Using the Riemann-Hilbert method, the paper systematically investigates the n-component generalized Sasa-Satsuma system. By utilizing the Tu scheme, we systematically construct the n-component generalized Sasa-Satsuma integrable hierarchy, and obtain the
Zhiguo Ren, Jing Yu, Lin Huang
doaj   +1 more source