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Exponential asymptotics and Stokes lines in nonlinear ordinary differential equations. (English) Zbl 0916.34017

Singularly perturbed nonlinear ordinary differential equations are considered. An application of the WKBJ-type ansatz to the late terms in the asymptotic expansion is presented. The proposed method is based on making the exponentials visible by optimally truncating the algebraic asymptotic series and the identification of Stokes lines is made. Several examples of the technique are given.

MSC:

34A34 Nonlinear ordinary differential equations and systems
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
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