Geodesic
On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa–Holm Equation
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: integrable hierarchies; Camassa–Holm equation; Bäcklund transformation. 
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}
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Henrik Aratyn; Jose Francisco Gomes; Abraham H. Zimerman. On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa–Holm Equation. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a69/

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