Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 070, 12 pages      hep-th/0610182
Contribution to the Proceedings of the O'Raifeartaigh Symposium

On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation

Henrik Aratyn a, Jose Francisco Gomes b and Abraham H. Zimerman b
a) Department of Physics, University of Illinois at Chicago, 845 W. Taylor St., Chicago, Illinois 60607-7059
b) Instituto de Física Teórica-UNESP, Rua Pamplona 145, 01405-900 São Paulo, Brazil

Received September 13, 2006, in final form October 05, 2006; Published online October 17, 2006

Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled by an angle θ 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 θ being 0, π/2 or taking any value in the interval 0 < θ < π/2. This construction induces Bäcklund transformations between solutions of the two-component Camassa-Holm model associated with different classes of reduction.

Key words: integrable hierarchies; Camassa-Holm equation; Bäcklund transformation.

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