Generalized WKB Method with Applications to Problems of Propagation in Nonhomogeneous Media

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Abstract
A generalized WKB method is derived for the solution of the general second‐order differential equation. The problem is reduced to the solution of two coupled first‐order differential equations. By an appropriate choice of auxiliary functions, the coupling coefficients may be made sufficiently small to facilitate the solution of the coupled equations. It is shown that these solutions can be used in a range of problems in which the regular WKB solutions fail. These generalized solutions may also be used to derive asymptotic expansions of known functions. Applications of the method to higher‐order differential equations are indicated, and solutions to the nonlinear Riccati equation are considered.