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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 096, 8 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.096 (Mi sigma124) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Restricted Flows and the Soliton Equation with Self-Consistent Sources

Runliang Lina, Haishen Yaob, Yunbo Zenga

a Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China
b Dept. of Math and Computer Science, QCC, The City University of New York, USA
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DOI: https://doi.org/10.3842/SIGMA.2006.096
Abstract: The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Bäcklund transformation for the restricted flows (by V. B. Kuznetsov et al.), we constructed two types of Darboux transformations for the KdV equation with self-consistent sources (KdVES). These Darboux transformations are used to get some explicit solutions of the KdVES, which include soliton, rational, positon, and negaton solutions.
Keywords: the KdV equation with self-consistent sources; restricted flows; Lax pair; Darboux transformation; soliton solution.
Received: October 28, 2006; in final form December 22, 2006; Published online December 30, 2006
Bibliographic databases:
Document Type: Article
MSC: 35Q51; 35Q53; 37K10
Language: English
Citation: Runliang Lin, Haishen Yao, Yunbo Zeng, “Restricted Flows and the Soliton Equation with Self-Consistent Sources”, SIGMA, 2 (2006), 096, 8 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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