Integrable Flows on Null Curves in the Anti-de Sitter 3-Space

We formulate integrable flows related to the KdV hierarchy on null curves in the anti-de Sitter 3-space ($\mathrm{A}\mathrm{d}\mathrm{S}$). Exploiting the specific properties of the geometry of $\mathrm{A}\mathrm{d}\mathrm{S}$, we analyze their interrelationships with Pinkall flows in centro-affine geometry. We show that closed stationary solutions of the lower order flow can be explicitly found in terms of periodic solutions of a Lamé equation. In addition, we study the evolution of non-stationary curves arising from a 3-parameter family of periodic solutions of the KdV equation.