Nora Gavrea (University of Leeds) – Kinks and Integrability

Abstract: Topological solitons are smooth, localized, finite-energy solutions of nonlinear PDEs arising in field theory. They are topologically stable in the sense that they cannot be continuously deformed into a constant solution without requiring infinite energy, and are characterized by an integer called the topological degree. The simplest examples of topological solitons are kinks in one spatial dimension. I will discuss their construction and properties, including the Bogomolny argument, which gives a lower bound on the energy in terms of the topological degree. For certain special equations, it is possible to generate explicit multi-soliton solutions systematically. In these rare situations, the system is called integrable. As an example of this, I will discuss sine-Gordon kinks.