2023/11/18 by Emilio Musso, Musso, Emilio, Álvaro Pámpano +1
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2311.11137
openalex publication_date 2023/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate integrable flows related to the KdV hierarchy on null curves in the anti-de Sitter 3-space (\rm AdS). Exploiting the specific properties of the geometry of \rm AdS, 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.