Abstract
We study the high-frequency asymptotics for the solution of the modified Helmholtz equation, in a quarter plane and subject to a specific Neumann condition, as an illustration of the procedure to extract the asymptotics via Fokas' transform method. The approach is based on Fokas' integral representation of the solution. Full asymptotic expansions of the solution are obtained by using Watson's lemma and the method of steepest descents for definite integrals.
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