Results 11 to 20 of about 303 (64)

Infinite dimension of solutions of the Dirichlet problem

Open Mathematics, 2015
It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.
Ryazanov Vladimir
doaj   +1 more source

Stability of the Periodic Toda Lattice in the Soliton Region [PDF]

, 2008
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the periodic (and slightly more generally of the quasi-periodic finite-gap) Toda lattice for decaying initial data in the soliton region.
Krueger, Helge, Teschl, Gerald
core   +3 more sources

Smoothed Analysis for the Conjugate Gradient Algorithm [PDF]

, 2016
The purpose of this paper is to establish bounds on the rate of convergence of the conjugate gradient algorithm when the underlying matrix is a random positive definite perturbation of a deterministic positive definite matrix.
Menon, Govind, Trogdon, Thomas
core   +1 more source

Rational Solutions of the Painlev\'e-II Equation Revisited [PDF]

, 2017
The rational solutions of the Painlev\'e-II equation appear in several applications and are known to have many remarkable algebraic and analytic properties. They also have several different representations, useful in different ways for establishing these
Miller, Peter D., Sheng, Yue
core   +3 more sources

Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schr\"odinger Equation II [PDF]

, 2015
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schr\"odinger equation. If $|n|
Yamane, Hideshi
core   +3 more sources

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

Boussinesq’s equation for water waves: the soliton resolution conjecture for Sector IV

Advanced Nonlinear Studies
We consider the Boussinesq equation on the line for a broad class of Schwartz initial data relevant for water waves. In a recent work, we identified ten main sectors describing the asymptotic behavior of the solution, and for each of these sectors we ...
Charlier Christophe, Lenells Jonatan
doaj   +1 more source

Infinite dimension of solutions for Dirichlet problem II [PDF]

, 2014
It is proved that the dimension of the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e.
Ryazanov, Vladimir
core  

Line bundles defined by the Schwarz function

, 2017
Cauchy and exponential transforms are characterized, and constructed, as canonical holomorphic sections of certain line bundles on the Riemann sphere defined in terms of the Schwarz function. A well known natural connection between Schwarz reflection and
Gustafsson, Björn, Putinar, Mihai
core   +1 more source

Long-time asymptotic behavior for the Hermitian symmetric space derivative nonlinear Schrödinger equation

Advanced Nonlinear Studies
Resorting to the spectral analysis of the 4 × 4 matrix spectral problem, we construct a 4 × 4 matrix Riemann–Hilbert problem to solve the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation.
Chen Mingming, Geng Xianguo, Liu Huan
doaj   +1 more source