Exponential asymptotics and Stokes lines in nonlinear ordinary differential equations

Abstract

A technique for calculating exponentially small terms beyond all orders in singularly perturbed ordinary differential equations is presented. The approach is based on the application of a WKBJ–type ansatz to the late terms in the naive asymptotic expansion and the identification of Stokes lines, and is closely related to the well–known Stokes line–smoothing phenomenon in linear ordinary differential equations. The method is illustrated by application to examples.