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

H. Aratyn; J. F. Gomes; A. H. Zimerman

doi:10.3842/SIGMA.2006.070

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

High Energy Physics - Theory 2008-12-19 v2 Mathematical Physics math.MP Exactly Solvable and Integrable Systems

Authors: H. Aratyn , J. F. Gomes , A. H. Zimerman

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Abstract

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.

Keywords

AKNS hierarchy negative flow two-component Camassa-Holm equation gauge copies reductions Bäcklund transformations

Cite

@article{arxiv.hep-th/0610182,
  title  = {On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation},
  author = {H. Aratyn and J. F. Gomes and A. H. Zimerman},
  journal= {arXiv preprint arXiv:hep-th/0610182},
  year   = {2008}
}

Comments

This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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

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