Promotion lecture in mathematics, Martin Hallnäs

Abstract: The sG-equation is a second order non-linear partial differential equation in two variables with many remarkable properties and interesting applications. It first appeared in classical works on surfaces of constant negative curvature and in the 1970s it became one of the main examples in the theory of solitons. In this talk, I will introduce the sG-equation, indicate some of its many special properties and applications and sketch some more recent developments on a particle-soliton correspondence for the sG-equation.