Abstract
This book deals with asymptotic solutions of linear and nonlinear equations which decay as h → 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions φ(x) exp {iS(x)/h}, x ∈ ℝ3, where S(x) is complex, and Im S(x) ≥ 0. When the phase S(x) is real (Im S(x) = 0), the method for obtaining asymptotics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case Im S(x) ≥ 0 and develop the method for a wide class of problems in mathematical physics.
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© 1994 Springer Basel AG
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Maslov, V.P. (1994). Introduction. In: The Complex WKB Method for Nonlinear Equations I. Progress in Physics, vol 16. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8536-2_1
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DOI: https://doi.org/10.1007/978-3-0348-8536-2_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9669-6
Online ISBN: 978-3-0348-8536-2
eBook Packages: Springer Book Archive