Wave motion is found everywhere: sound waves, water waves, electromagnetic waves, traffic waves and Mexican waves are just some examples. The mathematical description of wave motion can be fairly straightforward, as with the oscillations of a guitar string for example, but as more physical effects are allowed for the theory becomes more complicated.

In this project the aim would be to look at some well-known mathematical equations that describe different aspects of wave motion, to find out how they are solved and to look at different types of solutions. Two examples are Burgers’ equation and the Korteweg de Vries (KdV) equation.

This project would be almost entirely analytical but could include illustrations using Maple. Take a look at the animation at the link below – it shows two solitons (possible solutions of the KdV equation) moving at different speeds, interacting, then emerging as though one had passed through the other.

http://www.math.uwaterloo.ca/~kglamb/course_animations/KdV_inter.gif

Supervisor: Dr David Graham