6 citations · 8 across the 7 of their papers we have counts for
9 papers
An example of Newton's method for an equation in Gevrey series
Alexander Getmanenko
In the context of complex WKB analysis, we discuss a one-dimensional Schrödinger equation where , $Q_1(…
Microlocal properties of sheaves and complex WKB
Alexander Getmanenko, Dmitry Tamarkin
Kashiwara-Schapira style sheaf theory is used to justify analytic continuability of solutions of a Laplace transformed Schroedinger equation with a small parameter. This partially…
Shatalov-Sternin's construction of complex WKB solutions and the choice of integration paths
Alexander Getmanenko
We re-examine Shatalov-Sternin's proof of existence of resurgent solutions of a linear ODE. In particular, we take a closer look at the "Riemann surface" (actually, a two-dimension…
Resurgent analysis of the Witten Laplacian in one dimension -- II
Alexander Getmanenko
The Witten Laplacian in one dimension is studied further by methods of resurgent analysis in order to approach Fukaya's conjectures relating WKB asymptotics and disc instantons. In…
Shatalov-Sternin's construction of complex WKB solutions and the associated Riemann surface
Alexander Getmanenko
We re-examine Shatalov-Sternin's proof of existence of resurgent solutions of a linear ODE. In particular, we take a closer look at the "Riemann surface" (actually, a two-dimension…
Resurgent Analysis of the Witten Laplacian in One Dimension
Alexander Getmanenko
The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the…