Restricted Flows and the Soliton Equation with Self-Consistent Sources

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 transf...

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Veröffentlicht in:	Symmetry, integrability and geometry, methods and applications integrability and geometry, methods and applications, 2006-01, Vol.2, p.096
1. Verfasser:	Lin, Runliang
Format:	Artikel
Sprache:	eng
Schlagworte:	Darboux transformation Lax pair restricted flows soliton solution the KdV equation with self-consistent sources
Online-Zugang:	Volltext
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Zusammenfassung:	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.
ISSN:	1815-0659 1815-0659
DOI:	10.3842/SIGMA.2006.096