• DOI:10.1063/1.533420
• Corpus ID: 53368365

Integration of the soliton hierarchy with self-consistent sources

@article{Zeng2000IntegrationOT,
  title={Integration of the soliton hierarchy with self-consistent sources},
  author={Yunbo Zeng and Wenxiu Ma and Runliang Lin},
  journal={Journal of Mathematical Physics},
  year={2000},
  volume={41},
  pages={5453-5489}
}

• Yunbo Zeng, Wenxiu Ma, Runliang Lin
• Published 21 July 2000
• Physics
• Journal of Mathematical Physics

In contrast with the soliton equations, the evolution of the eigenfunctions in the Lax representation of soliton equation with self-consistent sources (SESCS) possesses singularity. We present a general method to treat the singularity to determine the evolution of scattering data. The AKNS hierarchy with self-consistent sources, the MKdV hierarchy with self-consistent sources, the nonlinear Schrodinger equation hierarchy with self-consistent sources, the Kaup–Newell hierarchy with self-consistent sources and the derivative nonlinear Schrodinger equation hierarchy with self-consistent sources are integrated directly by using the inverse scattering method. The N soliton solutions for some SESCS are presented. It is shown that the insertion of a source may cause the variation of the velocity of soliton. This approach can be applied to all other (1+1)-dimensional soliton hierarchies.