On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?
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Resumo
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.
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Bäcklund transformation, Camassa-Holm equation, Integrable hierarchies
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Inglês
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), v. 2., 12 p., 2006.
