Discrete Helmholtz equation and the interaction of two perpendicular semi-infinite boundaries: one equation with tree unknown functions.

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• Anastasia Kisil (University of Manchester)
• Monday 06 February 2023, 15:30-16:15
• Seminar Room 1, Newton Institute.

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MWSW01 - Canonical scattering problems

In this talk we are interested in solving the discrete Helmholtz equation on a square lattice with two perpendicular semi-infinite boundary conditions. The interaction of the two boundary forms an interesting multiple scattering problem which leads to a new equation to solve. This is a generalisation of the classical Wiener—Hopf equation, now in two variables and with three unknown function. A solution method for this type of equation will be presented by defining an underlining manifold that links the two variables.  Next the analyticity regions of unknown functions is extended and that allows to simplify the problem. As the result the problem is fully solvable in terms of Cauchy type integrals which is surprising since this is not always possible for such complicated type of problems. Some toy examples are presented to illustrate the method.

This talk is part of the Isaac Newton Institute Seminar Series series.

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