We revisit the Helmholts equation in a quarter-plane in the framework of the Riemann-Hilbert approach to linear boundary value problems suggested in late 90s by A. Fokas. We show the role of the Sommerfeld radiation condition in Fokas's scheme.
The transition between the gap probabilities from the Pearcey to the Airy process; a Riemann-Hilbert approach
Dirichlet-to-Neumann and Neumann-to-Dirichlet methods for bound states of the Helmholtz equation
Boundary perturbations and the Helmholtz equation in three dimensions
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