On Exact WKB Analysis for Painleve Equations

On the exact WKB analysis of microdifferential operators of WKB type ∗ Takashi AOKI

Exact WKB analysis of second-order non-homogeneous linear ordinary differential equations

In this paper we consider the exact WKB analysis of a second-order non-homogeneous linear ordinary differential equation with a large parameter. We give a geometric criterion which guarantees the Borel summability of formal solutions of a non-homogeneous equation; this criterion is described in terms of exact steepest descent paths introduced in [AKT2]. An example related to the BNR equation ([...

On the Exact Wkb Analysis for the Third Order Ordinary Differential Equations with a Large Parameter By

n-th order with n 2 has not yet been well established; its local aspect is clari ed under the assumption that the discriminant of the characteristic equation is of simple zeros ([AKT, Theorem 1.4 and Theorem 1.6]), but its global aspect is far from complete understanding ([BNR], [AKT, Section 2]). The purpose of this paper is to examine the validity of our Ansatz concerning the Stokes geometry ...

On the Exact Solution for Nonlinear Partial Differential Equations

In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...

QHJ, WKB and exact quantisation

We present a simple derivation of the WKB quantisation condition using the quantum Hamilton-Jacobi formalism and propose an exact quantisation condition within this formalism for integrable models in higher dimensions.