DescriptionTopological solitons provide description of classical objects that arise in many applications of mathematics. Their energy density is localised in a region of space. Such objects are stable with respect to small perturbations with the stability provided by topological considerations. In this project the students will look first at some simple nonlinear field theories and their classical solutions. Such solutions are often related to harmonic maps. Then the students will perform various topological considerations to see that the maps, interpreted as solitons, guarantee the stability of these solitons. At this stage the project can develop in various ways: some concrete applications, some properties of solitons, some numerical work..... PrerequisitesAnalysis in Many Variables II, Mathematical Physics II.ResourcesThere are many articles on the web and there are even some books on this topic. I can discuss them with interested students and then suggest specific things to read (as this will depend which ideas the students want to develop in this project). |
email: Wojtek Zakrzewski