
SIGMA 2 (2006), 096, 8 pages nlin.SI/0701003
https://doi.org/10.3842/SIGMA.2006.096
Contribution to the Vadim Kuznetsov Memorial Issue
Restricted Flows and the Soliton Equation with SelfConsistent Sources
Runliang Lin ^{a}, Haishen Yao ^{b} and Yunbo Zeng ^{a}
^{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
Received October 28, 2006, in final form December 22, 2006; Published online December 30, 2006
Abstract
The KdV equation is used as an example to illustrate the
relation between the restricted flows and the soliton equation
with selfconsistent 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 selfconsistent sources
(KdVES). These Darboux transformations are used to get some
explicit solutions of the KdVES, which include soliton, rational,
positon, and negaton solutions.
Key words:
the KdV equation with selfconsistent sources; restricted flows; Lax pair; Darboux transformation; soliton solution.
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