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Teoreticheskaya i Matematicheskaya Fizika, 2017, Volume 191, Number 2, Pages 275–290
DOI: https://doi.org/10.4213/tmf9197 (Mi tmf9197) 		 
This article is cited in 14 scientific papers (total in 14 papers)

The Darboux transformation for WKI system

Yongshuai Zhanga, Deqin Qiub, Yi Chenga, Jingsong Heb

a School of Mathematical Sciences, University of Science and Technology of China, Hefei, China
b Mathematics Department, Faculty of Science, Ningbo University, Ningbo, China
Full-text PDF (661 kB) Citations (14)
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DOI: https://doi.org/10.4213/tmf9197
Abstract: Based on a conservation law, we construct a hodograph transformation for the Wadati–Konno–Ichikawa (WKI) equation, which implies that the WKI equation is equivalent to a modified WKI (mWKI) equation. Applying the Darboux transformation to the mWKI equation, we show that in both the focusing and defocusing cases, the mWKI equation admits an analytic bright soliton solution from the vacuum and the collisions of $n$ solitons are elastic based on the asymptotic analysis. In addition, we find that the mWKI equation still admits the breather and rogue wave solutions, although a modulation instability does not exist for it.
Keywords: Darboux transformation, Wadati–Konno–Ichikawa system, hodograph transformation, soliton, rogue wave, modulation instability.
Funding agency Grant number
National Natural Science Foundation of China 11271210
K. C. Wong Magna Fund (Ningbo University)
This research is supported by the National Science Foundation of China (Grant No. 11271210) and the K. C. Wong Magna Fund in Ningbo University.
Received: 25.03.2016
Revised: 21.04.2016
English version:
Theoretical and Mathematical Physics, 2017, Volume 191, Issue 2, Pages 710–724
DOI: https://doi.org/10.1134/S0040577917050117
Bibliographic databases:
PACS: 02.30.Ik,03.75.Lm,42.65.Tg
Language: Russian
Citation: Yongshuai Zhang, Deqin Qiu, Yi Cheng, Jingsong He, “The Darboux transformation for WKI system”, TMF, 191:2 (2017), 275–290; Theoret. and Math. Phys., 191:2 (2017), 710–724
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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