Integrable flows on null curves in the Anti-de Sitter 3-space

Integrable flows on null curves in the Anti-de Sitter 3-space

We formulate integrable flows related to the Korteweg–De Vries (KdV) hierarchy 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 stati...

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Veröffentlicht in:Nonlinearity 2024-11, Vol.37 (11), p.115015
Hauptverfasser: Musso, Emilio, Pámpano, Álvaro
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Sprache:eng
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33E05
33E10
37K10
53B30
Anti-de Sitter space
integrable flows
KdV equation
Lamé equation
null curves
special functions
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Pámpano, Álvaro
description We formulate integrable flows related to the Korteweg–De Vries (KdV) hierarchy 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 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.
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subjects 33E05
33E10
37K10
53B30
Anti-de Sitter space
integrable flows
KdV equation
Lamé equation
null curves
special functions
title Integrable flows on null curves in the Anti-de Sitter 3-space
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