# 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} }

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…

## 177 Citations

Solving soliton equations with self-consistent sources by method of variation of parameters

- PhysicsAppl. Math. Comput.
- 2010

Two new integrable couplings of the soliton hierarchies with self-consistent sources

- Physics
- 2010

A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with l(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys.…

Conservation laws and soliton solutions for a nonlinear Schrödinger equation with self-consistent sources in plasmas

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- 2010

Via symbolic computation, this paper investigates a nonlinear Schrodinger (NLS) equation with self-consistent sources (SCSs), which can describe the nonlinear interaction between an electrostatic…

Solving the hierarchy of the nonisospectral KdV equation with self-consistent sources via the inverse scattering transform

- Physics, Mathematics
- 2008

The hierarchy of the nonisospectral KdV equation with self-consistent sources is derived. N-soliton solutions of the hierarchy are obtained through the inverse scattering transform. We develop new…

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- 2014

In the paper, Ablowitz—Ladik hierarchy with new self-consistent sources is investigated. First the source in the hierarchy is described as nn+1, where n is related to the Ablowitz—Ladik spectral…

Restricted Flows and the Soliton Equation with Self-Consistent Sources

- Physics
- 2006

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…

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