# Diffraction by a quarter-plane. Links between the functional equation, additive crossing and Lam\'e functions

@article{Assier2020DiffractionBA, title={Diffraction by a quarter-plane. Links between the functional equation, additive crossing and Lam\'e functions}, author={Raphael Assier and Andrey V. Shanin}, journal={arXiv: Analysis of PDEs}, year={2020} }

In our previous work (Assier & Shanin, QJMAM, 2019), we gave a new spectral formulation in two complex variables associated with the problem of diffraction by a quarter-plane. In particular, we showed that the unknown spectral function satisfies a condition of additive crossing about its branch set. In this paper, we study a very similar class of spectral problem, and show how the additive crossing can be exploited in order to express its solution in terms of Lame functions. The solution…

## One Citation

### Analytical continuation of two-dimensional wave fields

- MathematicsProceedings of the Royal Society A
- 2021

Wave fields obeying the two-dimensional Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied and it is shown that such wave fields admit an analytical continuation into the domain of two complex coordinates.

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