On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation

Details On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation

2006-10-16

arxiv.org/abs/hep-th/0610182v2

SIGMA 2:070,2006

Physics

High Energy Physics

High Energy Physics - Theory

This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (

Scientific paper

10.3842/SIGMA.2006.070

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 B\"{a}cklund transformations between solutions of the two-component Camassa--Holm model associated with different classes of reduction.

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