Introduction

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.