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Host: University of Birmingham
Homepage: http://www.lms.ac.uk/activities/research_meet_com/short_course/06_app.html
Organizers: J. Billingham, A.C. King
Description:
Wave phenomena occur in many important physical and chemical systems. We shall begin by describing the simplifications
available for small-amplitude linear water waves, and how dispersion affects their propagation. We shall also study linear shallow
water waves, and, in the final part of the course, consider how basic linear shallow water waves are modified by the introduction of
weak nonlinearity. This leads to the Kortweg-de Vries equation, which we shall learn how to solve using the inverse scattering
transform, introducing the concept of a soliton solution along the way.
The remainder of the course is concerned with nonlinear gas dynamics, waves of chemical reaction and diffraction. We shall study nonlinear gas dynamics as an example of a system in which wave steepening causes shock waves to form. In contrast, chemical waves form through a balance between chemical reaction and molecular diffusion. In studying diffraction, we shall see how the Wiener-Hopf technique can be used to analyse how light and sound interact with sharp edges. We conclude the course by studying nonlinear water waves, concentrating on some simple instability mechanisms.
The meeting is aimed at research students working in the areas of continuum mechanics and/or mathematical modelling.
Date received: December 24, 2000
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