Geometric null curve flows and integrable systems in Lorentz space

The focus of this dissertation is to study group-invariant soliton equations in Lorentzian flat symmetric space and their integrability structure arising from flows of non-stretching null curves. In our thesis, first of all, basic definitions and theorems that we need to use in the following chapters were considered. Secondly, geometric null curve flows and it's integrable systems were showed in two ways: one for the algebraic way and another one for the geometric way. The rest of our thesis, Burger's, Airy, Gradient and Hamiltonian flows were found for null curves.