We formulate integrable flows related to the Korteweg–De Vries (KdV) hier- archy on null curves in the anti-de Sitter 3-space (AdS). Exploiting the specific properties of the geometry of AdS, we analyze their interrelationships with Pinkall flows in centro-affine geometry. We show that closed stationary solu- tions 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.
Integrable flows on null curves in the Anti-de Sitter 3-space / Musso, Emilio; Pámpano, Álvaro. - In: NONLINEARITY. - ISSN 0951-7715. - ELETTRONICO. - 37:11(2024), pp. 1-38. [10.1088/1361-6544/ad7d58]
Integrable flows on null curves in the Anti-de Sitter 3-space
Musso, Emilio;
2024
Abstract
We formulate integrable flows related to the Korteweg–De Vries (KdV) hier- archy on null curves in the anti-de Sitter 3-space (AdS). Exploiting the specific properties of the geometry of AdS, we analyze their interrelationships with Pinkall flows in centro-affine geometry. We show that closed stationary solu- tions 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.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2993327