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Zbl 0972.35128
Lin, R.; Zeng, Y.; Ma, W.-X.
Solving the KdV hierarchy with self-consistent sources by inverse scattering method. (English)
[J] Physica A 291, No.1-4, 287-298 (2001). ISSN 0378-4371

Summary: The evolution of the eigenfunctions in the Lax representation of the KdV hierarchy with self-consistent sources possesses singularity. By proposing a method to treat the singularity to determine the evolution of scattering data, the KdV hierarchy with self-consistent sources is integrated by the inverse scattering method. The soliton solutions of these equations are obtained. It is shown that the insertion of a source may cause the variation of the speed of soliton. This approach can be applied to other (1+1)-dimensional soliton hierarchies.

MSC 2000:: *35Q53 KdV-like equations
35Q51 Solitons

Keywords: eigenfunction evolution; Lax representation; solitons

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