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- Title
Integrable Semi-discrete Kundu-Eckhaus Equation: Darboux Transformation, Breather, Rogue Wave and Continuous Limit Theory.
- Authors
Zhao, Hai-qiong; Yuan, Jinyun; Zhu, Zuo-nong
- Abstract
To get more insight into the relation between discrete model and continuous counterpart, a new integrable semi-discrete Kundu-Eckhaus equation is derived from the reduction in an extended Ablowitz-Ladik hierarchy. The integrability of the semi-discrete model is confirmed by showing the existence of Lax pair and infinite number of conservation laws. The dynamic characteristics of the breather and rational solutions have been analyzed in detail for our semi-discrete Kundu-Eckhaus equation to reveal some new interesting phenomena which was not found in continuous one. It is shown that the theory of the discrete system including Lax pair, Darboux transformation and explicit solutions systematically yields their continuous counterparts in the continuous limit.
- Subjects
DISCRETE systems; DISCRETE element method; ROGUE waves; NUMERICAL analysis; MATHEMATICAL analysis
- Publication
Journal of Nonlinear Science, 2018, Vol 28, Issue 1, p43
- ISSN
0938-8974
- Publication type
Article
- DOI
10.1007/s00332-017-9399-9