Constant speed flows and the nonlinear Schrödinger equation

Abstract

This thesis demonstrates how the geometric connection between the integrable Heisenberg spin equation, the nonlinear Schrödinger equation and fluid flows with constant velocity magnitude along individual streamlines may be exploited. Specifically, we are able to construct explicitly the complete class of constant speed flows where the constant pressure surfaces constitute surfaces of revolution. This class is undoubtedly important as it contains many of the specific cases discussed earlier by other authors.