Solitons are solutions of nonlinear equations, which describe localised objects which can propagate for a long time without deforming, and losing their shape. Soliton-like solutions appear in different physical systems, in particular in different systems in solid state physics. In this projects, you will learn the basic ideas behind the existence of solitons, and see how these ideas are realised in real world systems. For example, you can look at some classical solitons which were discovered in Bose-Einstein condensates of atoms, or optical solitons. Another potential direction in which the project can be developed are the quantum aspects of solitons, such as semi-classical quantisation. Also, applications of solitons to describe nonperturbative phenomena in quantum field theory are a direction suited for those who have taken and enjoyed quantum field theory lectures.
It is good (but not necessary) to take the Solitons IV module. If you are interested in learning about quantum aspects of solitons then the Quantum Mechanics III module is necessary.