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SIGMA 2 (2006), 070, 12 pages hep-th/0610182
https://doi.org/10.3842/SIGMA.2006.070
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
Abstract
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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