Research in The Wiener-Hopf and Related Techniques

The Wiener-Hopf technique has proved to be an immensely important method in engineering and mathematical physics. It offers one of the very few approaches to obtaining exact solutions to complex integral equations. An enormous variety of physically important problems can be cast into this form of equation; fields of application include diffraction of acoustic, elastic and electromagnetic waves, fracture mechanics, high speed and slow flow problems, fluid-structure interactions, diffusion models, crystal growth, geophysical applications, mathematical finance to name but a few. The solution method entails an elegant and quite sophisticated procedure employing certain analyticity properties of complex functions. Students with an interest in mathematical methods, including Fourier transforms, complex variable theory, asymptotics etc., may find this area appealing.

Ongoing research at Manchester concerns both the application of the Wiener-Hopf technique and its extension to coupled systems or models of complicated form.

Members of staff involved