Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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 Self-Consistent 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 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.

Key words: the KdV equation with self-consistent sources; restricted flows; Lax pair; Darboux transformation; soliton solution.

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