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Integrable Semi-discrete Kundu–Eckhaus Equation: Darboux Transformation, Breather, Rogue Wave and Continuous Limit Theory
- Source :
- Journal of Nonlinear Science. 28:43-68
- Publication Year :
- 2017
- Publisher :
- Springer Science and Business Media LLC, 2017.
-
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 :
- Conservation law
Integrable system
Breather
Applied Mathematics
Mathematical analysis
General Engineering
01 natural sciences
010305 fluids & plasmas
Discrete system
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Transformation (function)
Modeling and Simulation
0103 physical sciences
Lax pair
Limit (mathematics)
Rogue wave
010306 general physics
Nonlinear Sciences::Pattern Formation and Solitons
Mathematics
Subjects
Details
- ISSN :
- 14321467 and 09388974
- Volume :
- 28
- Database :
- OpenAIRE
- Journal :
- Journal of Nonlinear Science
- Accession number :
- edsair.doi...........a39e961eb70e08fae78751753eef27c7