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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 070, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.070 (Mi sigma98) 		 
This article is cited in 21 scientific papers (total in 21 papers)

On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa–Holm Equation

Henrik Aratyna, Jose Francisco Gomesb, Abraham H. Zimermanb

a Department of Physics, University of Illinois at Chicago, 845 W. Taylor St., Chicago, Illinois 60607-7059
b Instituto de Física Teórica-UNESP, Rua Pamplona 145, 01405-900 São Paulo, Brazil
Full-text PDF (223 kB) Citations (21)
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DOI: https://doi.org/10.3842/SIGMA.2006.070
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 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.
Received: September 13, 2006; in final form October 5, 2006; Published online October 17, 2006
Bibliographic databases:
Document Type: Article
MSC: 37K10; 35Q53; 53A07; 53B50
Language: English
Citation: 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”, SIGMA, 2 (2006), 070, 12 pp.
Citation in format AMSBIB
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\paper On a~Negative Flow of the AKNS Hierarchy and Its Relation to a~Two-Component Camassa--Holm Equation
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    		Symmetry, Integrability and Geometry: Methods and Applications
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