On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation - Aratyn, H.; Gomes, J.F.; Zimerman, A.H. (Symmetry, Integrability and Geometry: Methods and Applications, 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.