Nonlinear Waves: Theory and Simulations

Many physical processes exhibit some form of nonlinear wave phenomena. However diverse they are (e.g. from engineering to finance), however small they are (e.g. from atomic to cosmic scales), they all emerge from hyperbolic partial differential equations (PDEs). This course explores aspects of hyperbolic PDEs leading to the formation of shocks and solitary waves, with a strong emphasis on systems of balance laws (e.g. mass, momentum, energy) owing to their prevailing nature in Nature. In addition to presenting key theoretical concepts, the course is designed to offer computational strategies to explore the rich and fascinating world of nonlinear wave phenomena.

By the end of this course, participants dealing with wave-like phenomena in their research field of interest should be able to identify components that can trigger front-like structures (e.g. shocks, solitons) and be able to explore their motion numerically. Whilst the course is aimed at graduate students with an engineering/physics background, biologists interested in wave phenomena in biological systems (e.g. neurones, arteries, cells) are also welcome. However, it is assumed that participants have prior knowledge of maths for engineers and physicists.