Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Its, Alexander R."'
We obtain rigorous large time asymptotics for the Landau-Lifshitz equation in the soliton free case by extending the nonlinear steepest descent method to genus 1 surfaces. The methods presented in this paper pave the way to rigorous analysis of other
Externí odkaz:
http://arxiv.org/abs/2405.17662
This paper is the first in a forthcoming series of works where the authors study the global asymptotic behavior of the radial solutions of the 2D periodic Toda equation of type $A_n$. The principal issue is the connection formulae between the asympto
Externí odkaz:
http://arxiv.org/abs/2309.16550
In previous articles we have studied the A_n tt*-Toda equations (topological-antitopological fusion equations of Toda type) of Cecotti and Vafa, giving details mainly for n=3. Here we give a proof of the existence and uniqueness of global solutions f
Externí odkaz:
http://arxiv.org/abs/2302.04597
This paper, the third in a series, completes our description of all (radial) solutions on C* of the tt*-Toda equations, using a combination of methods from p.d.e., isomonodromic deformations (Riemann-Hilbert method), and loop groups. We place these g
Externí odkaz:
http://arxiv.org/abs/1707.00259
In Part I (arXiv:1209.2045) we computed the Stokes data, though not the "connection matrix", for the smooth solutions of the tt*-Toda equations whose existence we established by p.d.e. methods. Here we give an alternative proof of the existence of so
Externí odkaz:
http://arxiv.org/abs/1312.4825
We describe all smooth solutions of the two-function tt*-Toda equations (a version of the tt* equations, or equations for harmonic maps into SL(n,R)/SO(n)) in terms of (i) asymptotic data, (ii) holomorphic data, and (iii) monodromy data. This allows
Externí odkaz:
http://arxiv.org/abs/1209.2045
Autor:
Its, Alexander R., Takhtajan, Leon A.
We introduce a dbar-formulation of the orthogonal polynomials on the complex plane, and hence of the related normal matrix model, which is expected to play the same role as the Riemann-Hilbert formalism in the theory of orthogonal polynomials on the
Externí odkaz:
http://arxiv.org/abs/0708.3867
Publikováno v:
Physica D 152-153 (2001), 199-224
This paper, a continuation of math.CO/9909169, connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a Riemann-Hilbert problem and an associated system of integrable PDEs. In particular, we
Externí odkaz:
http://arxiv.org/abs/nlin/0004018
Publikováno v:
Random Matrices and their Applications, eds. P. Bleher and A. Its, Cambridge University Press, New York, 2001, pgs. 245-258.
It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for the eigenvalues of a certain direct sum of Gaussian unitary ensembles s
Externí odkaz:
http://arxiv.org/abs/math/9909169