Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations

Complex Variable and Fourier Transforms: 1.1 Introduction; 1.2 Complex variable theory; 1.3 Analytic functions defined by integrals; 1.4 The Fourier integral; 1.5 The wave equation; 1.6 Contour integrals of a certain type; 1.7 The Wiener-Hopf procedure; Miscellaneous examples and results I Basic Procedures: Half-Plane Problems: 2.1 Introduction; 2.2 Jones's method; 2.3 A dual integral equation method; 2.4 Integral equation formulations; 2.5 Solution of the integral equations; 2.6 Discussion of the solution; 2.7 Comparison of methods; 2.8 Boundary conditions specified by general functions; 2.9 Radiation-type boundary conditions; Miscellaneous examples and results II Further Wave Problems: 3.1 Introduction; 3.2 A plane wave incident on two semi-infinite parallel planes; 3.3 Radiation from two parallel semi-infinite plates; 3.4 Radiation from a cylindrical pipe; 3.5 Semi-infinite strips parallel to the walls of a duct; 3.6 A strip across a duct; Miscellaneous examples and results III Extensions and Limitations of the Method: 4.1 Introduction; 4.2 The Hilbert problem; 4.3 General considerations; 4.4 Simultaneous Wiener-Hopf equations; 4.5 Approximate factorization; 4.6 Laplace's equation in polar co-ordinates; Miscellaneous examples and results IV Some Approximate Methods: 5.1 Introduction; 5.2 Some problems which cannot be solved exactly; 5.3 General theory of a special equation; 5.4 Diffraction by a thick semi-infinite strip; 5.5 General theory of another special equation; 5.6 Diffraction by strips and slits of finite width; Miscellaneous examples and results V The General Solution of the Basic Wiener-Hopf Problem: 6.1 Introduction; 6.2 The exact solution of certain dual integral equations; Miscellaneous examples and results VI Bibliography Index.