Solving the KdV hierarchy with self-consistent sources by inverse scattering method

The evolution of the eigenfunctions in the Lax representation of the KdV hi erarchy with self-consistent sources possesses singularity. By proposing a method to treat the singularity to determine the evolution of scattering da ta, the KdV hierarchy with self-consistent sources is integrated by the inv erse scattering method. The soliton solutions of these equations are obtain ed. It is shown that the insertion of a source may cause the variation of t he speed of soliton. This approach can be applied to other (1 + 1)-dimensio nal soliton hierarchies. (C) 2001 Elsevier Science B.V. All rights reserved .