Project description
Integrable equations, that include nonlinear Schrodinger, KdV, Painlevé equations are shown to play significant roles in a wide range of physical theories such as quantum gravity, random matrix theory, nonlinear optics. They are shown to possess remarkable properties. Two of such properties are the Hamiltonian structure (classical and well-known) and discrete symmetry groups (coming from a recent ground-breaking classification result by Sakai in 2001). This project aims to understand the relationship between this two interesting characteristic of Integrable equations.
Assumed knowledge
Linear algebra
Industry involvement
Note: You need to register interest in projects from different supervisors (not a number of projects with the one supervisor).
You must also contact each supervisor directly to discuss both the project details and your suitability to undertake the project.