Restricted Flows and the Soliton Equation with Self-Consistent Sources

Details Restricted Flows and the Soliton Equation with Self-Consistent Sources Restricted Flows and the Soliton Equation with Self-Consistent Sources

2006-12-30

arxiv.org/abs/nlin/0701003v1

SIGMA 2 (2006), 096, 8 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2006.096

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 Backlund 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.

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