1. Exact Solutions of Ablowitz—Ladik Hierarchy with Self-Consistent Sources Revisited and Reductions
- Author
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Jian-Bing Zhang, Qiu-Yuan Duan, Deng-yuan Chen, and Qi Li
- Subjects
Nonlinear system ,Hierarchy ,symbols.namesake ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Physics and Astronomy (miscellaneous) ,Inverse scattering transform ,symbols ,Applied mathematics ,Uniqueness ,Self consistent ,Nonlinear Sciences::Pattern Formation and Solitons ,Schrödinger's cat ,Mathematics - Abstract
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 problem, instead of the corresponding adjoint spectral problem. Then by means of the inverse scattering transform, the multi-soliton solutions for the hierarchy are obtained. Two reductions to the discrete mKdV and nonlinear Schrodinger hierarchies with self-consistent sources are considered by using the uniqueness of the Jost functions, as well as their N-soliton solutions.
- Published
- 2014