6 papers
Transition asymptotics for the real solutions of the sinh-Gordon Painlevé III equation
Kenta Miyahara, Maxim L. Yattselev
We consider solutions of the sinh-Gordon Painlevé III equation \[ u_{xx} + \frac{1}{x} u_x = \sinh u \] that are real on . They are parametrized by the monodromy param…
Reduction of Multiple Orthogonal Polynomials to Standard Orthogonal Polynomials
Roozbeh Gharakhloo, Maksim Kosmakov, Kenta Miyahara
In this article, we derive explicit formulae expressing multiple orthogonal polynomials in terms of standard orthogonal polynomials. We treat both the real-line and unit-circle set…
Long-time asymptotics of the autocorrelation function of the transverse Ising chain at the critical magnetic field Revisited
Noah Hout, Kenta Miyahara, Dustin Newland +1
Following the work of Deift and Zhou (DOI:10.1007/978-1-4615-2474-8_15), we analyze the long-time asymptotics of the autocorrelation function of the transverse Ising chain at the c…
Connection formulae for the radial Toda equations I
Martin A. Guest, Alexander R. Its, Maksim Kosmakov +2
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_…
Connection formulae for the radial Toda equations II
Martin A. Guest, Alexander R. Its, Maksim Kosmakov +2
This is a continuation of [arXiv:2309.16550] in which we computed the asymptotics near of all solutions of the radial Toda equation. In this article, we compute the as…
The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlevé III equation
Alexander R. Its, Kenta Miyahara, Maxim L. Yattselev
Motivated by the simplest case of tt*-Toda equations, we study the large and small asymptotics for of real solutions of the sinh-Godron Painlevé III() equation. The…