278 citations · 1.7k across the 68 of their papers we have counts for
8 papers · 1 filter
On Tracy-Widom distribution and the second Calogero-Painlevé system
Alexander Its, Andrei Prokhorov
The Calogero-Painlevé systems were introduced in 2001 by K. Takasaki as a natural generalization of the classical Painlevé equations to the case of the several Painlevé ``particles…
Periodic problem for the nonlinear Schroedinger equation
Vladimir Kotlyarov, Alexander Its
The paper offers the method of discovering of some class of solutions for the nonlinear Schroedinger equation. An algorithm of constructive solving of the Cauchy periodic problem w…
Asymptotics of a cubic sine kernel determinant
Thomas Bothner, Alexander Its
We study the one parameter family of Fredholm determinants of an integrable Fredholm operator acting on the…
Initial boundary value problem for the focusing NLS equation with Robin boundary condition: half-line approach
Alexander Its, Dmitry Shepelsky
We consider the initial boundary value problem for the focusing nonlinear Schrödinger equation in the quarter plane in the case of decaying initial data (for , as $x…
The Nonlinear Schrödinger Equation on the Interval
A. S. Fokas, A. R. Its
Let satisfy the Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation on the finite interval, , with , $g_{0}(t) =…
The nonlinear steepest descent approach to the asymptotics of the second Painleve transcendent in the complex domain
A. R. Its, A. A. Kapaev
The asymptotics of the generic second Painleve transcendent in the complex domain is found and justified via the direct asymptotic analysis of the associated Riemann-Hilbert proble…
Quasi-linear Stokes phenomenon for the second Painlevé transcendent
A. R. Its, A. A. Kapaev
Using the Riemann-Hilbert approach, we study the quasi-linear Stokes phenomenon for the second Painlevé equation . The precise description of the exponentially sm…
Random Words, Toeplitz Determinants and Integrable Systems. II
Alexander R. Its, Craig A. Tracy, Harold Widom
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 p…