The principal investigator will analyse the dynamics of topological defects in solutions of nonlinear field equations. These problems arise naturally in various physical contexts. In particular, vortex dynamics in superconductors, spiral waves in reaction-diffusion processes, grain boundaries and dislocation defects in models of convection, and the dynamics of topological singularities in nonlinear hyperbolic field theories of modern physics will be examined. The methodology to be employed is that of multiple-scale analysis which exploits the separaton of spatial scales multiple-scale analysis which that are instrinsic to these problems: the distance between defects is taken as large compared to their effective radii. This methodology has been successfully applied to the two-dimensional nonlinear Schroedinger equation, nonlinear heat equation, and nonlinear wave equation, and it is clear that their scope is sufficient to lead to new and useful insights in the physical problems to be studied in this project.
