Applications of Analytic and Geometric Methods to Nonlinear Differential Equations

In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton'' equations. (2) Twistor theory, using differential geometry, which has been used to solve t...