On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation

Abstract

Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled by an angle $\theta$ are constructed and then reduced to the two-component Camassa--Holm model. Only three different independent classes of reductions are encountered corresponding to the angle $\theta$ being 0, $\pi /2$ or taking any value in the interval $0<\theta <\pi /2$. This construction induces Bäcklund transformations between solutions of the two-component Camassa--Holm model associated with different classes of reduction.

This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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Cited by in corpus (6)

• A vectorial binary Darboux transformation of the first member of the negative part of the AKNS hierarchy
• Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy
• Deformations of N=2 super-conformal algebra and supersymmetric two-component Camassa-Holm equation
• 3D-consistency of negative flows
• Miura-reciprocal transformations and localizable Poisson pencils
• Neumann Type Integrable Reduction to the Negative-Order Coupled Harry--Dym Hierarchy