The WKB and Related Methods
In the method of matched asymptotic expansions studied in Chapter 2, the dependence of the solution on the boundary-layer coordinate was determined by solving the boundary-layer problem. In a similar way, when using multiple scales the dependence on the fast time scale was found by solving a differential equation. This does not happen with the WKB method because one begins with the assumption that the dependence is exponential. This is a reasonable expectation since many of the problems we studied in Chapter 2 ended up having an exponential dependence on the boundary-layer coordinate. Also, by making this assumption, we can significantly reduce the work necessary to find an asymptotic approximation of the solution.
KeywordsGeneral Solution Turning Point Travel Wave Solution Related Method Eikonal Equation
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