A Genus-3 Riemann-Hilbert Problem and Diffraction of a Wave by Two Orthogonal Resistive Half-Planes

作者：Antipov Yuri A^*

来源：Computational Methods and Function Theory, 2011, 11(2): 439-462.

• Riemann-Hilbert problem
• Riemann surfaces
• matrix factorization
• electromagnetic diffraction

Diffraction of a plane electromagnetic wave (E-polarization) by two orthogonal electrically resistive half-planes is analyzed. The physical problem reduces to a Riemann-Hilbert problem in the real axis for four pairs of analytic functions Phi(+)(j) (eta) (eta is an element of C+) and Phi(-)(j) (eta) = Phi(+)(j) (-eta) (eta is an element of C), j = 1; 2; 3; 4, where C+ and C- are the upper and lower half-planes. It is shown that the problem is equivalent to two scalar Riemann-Hilbert problems on a plane and a Riemann-Hilbert problem on a genus-3 hyperelliptic surface subject to a certain symmetry condition. A closed-form solution is derived in terms of singular integrals and the genus-3 Riemann Theta function.

• 出版日期2011