103 citations · 305 across the 12 of their papers we have counts for
12 papers
A Riemann-Hilbert Approach to the Heun Equation
Boris Dubrovin, Andrei Kapaev
We describe the close connection between the linear system for the sixth Painlevé equation and the general Heun equation, formulate the Riemann-Hilbert problem for the Heun functio…
Remark on repo and options
Andrei Kapaev
The general and special repo rates are related with the prices of the European call- and American put-options. The evaluation takes into account specific business models of the par…
On an isomonodromy deformation equation without the Painlevé property
Boris Dubrovin, Andrei Kapaev
We show that the fourth order nonlinear ODE which controls the pole dynamics in the general solution of equation compatible with the KdV equation exhibits two remarkable pr…
Asymptotics of the instantons of Painleve I
Stavros Garoufalidis, Alexander Its, Andrei Kapaev +1
The 0-instanton solution of Painlevé I is a sequence of complex numbers which appears universally in many enumerative problems in algebraic geometry, graph theory, matr…
Quasi-linear Stokes phenomenon for the Hastings-McLeod solution of the second Painlevé equation
A. A. Kapaev
Using the Riemann-Hilbert approach, we explicitly construct the asymptotic -function corresponding to the solution as to the second Painlevé…
Quasi-linear Stokes phenomenon for the Painlevé first equation
Andrei A. Kapaev
Using the Riemann-Hilbert approach, the -function corresponding to the solution of the first Painleve equation, , with the asymptotic behavior $y\sim\pm\sqrt{-x/6…