M2AM - NONLINEAR WAVES
This course considers the dynamics of continuous media, e.g. fluids. We will derive and analyse partial differential equations (PDEs) that can be used to describe nonlinear wave phenomena observed in nature and applications. Examples include formation and propagation of shock waves in gas dynamics, traffic flow and general conservation models encountered in biology, for example. The latter part of the course will consider the problem of water waves, develop the linear theory and also consider finite amplitude waves, ultimately leading to the celebrated Kortweg de-Vries equation that supports the formation of solitary waves. Throughout the course, reference will be made to experiments and images from experiments will be displayed and discussed.