Research in Integrable Systems and Mathematical Physics

Integrable systems is a branch of mathematics which has a long history but first came to prominance in the mid 1960's with the (mathematical) discovery of the soliton by Kruskal and Zabusky in connection with a dispersive shallow water wave problem. Since then this field has come to embrace many different aspects of mathematical physics. In this department there is currently a group of six academic staff working on a range of different problems in this area. Details of these are given below.

Every four years we organise a conference, under the acronym ISLAND, concentrating on one or more aspects of integrable systems. The next meeting is ISLAND III in 2007.

We are part of the UK-wide network "Classical and Quantum Integrability", funded by the London Mathematical Society.

  Topics
Christopher Athorne
Darboux transformations and integrable discrete systems
Hamiltonian systems
Lie symmetry theory
algebraic and geometric aspects
Mikhail Feigin Hadamard's problem
algebraic and geometric aspects
Frobenius manifolds and related topics
Claire Gilson bilinear methods and exact solutions
Darboux transformations and integrable discrete systems
Christian Korff the quantum inverse scattering method and representation theory
algebraic and geometric aspects
Jonathan Nimmo bilinear methods and exact solutions
Darboux transformations and integrable discrete systems
algebraic and geometric aspects
Ian Strachan Frobenius manifolds and related topics

 

Current research students

Sarah Croke, James Ferguson, Susan MacFarlane, Craig Sooman.

Details of the work of some former students is described here.