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The Darboux transformation for the Wadati–Konno–Ichikawa system

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, China

    Yongshuai Zhang & Yi Cheng

  2. Mathematics Department, Faculty of Science, Ningbo University, Ningbo, China

    Deqin Qiu & Jingsong He

  3. College of Mathematics and Statistics, Jishou University, Jishou, China

    Deqin Qiu

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  1. Yongshuai Zhang
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  2. Deqin Qiu
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  3. Yi Cheng
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  4. Jingsong He
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Correspondence to Deqin Qiu.

Additional information

This research is supported by the National Science Foundation of China (Grant No. 11271210) and the K. C. Wong Magna Fund in Ningbo University.

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 191, No. 2, pp. 275–290, May, 2017.

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Zhang, Y., Qiu, D., Cheng, Y. et al. The Darboux transformation for the Wadati–Konno–Ichikawa system. Theor Math Phys 191, 710–724 (2017). https://doi.org/10.1134/S0040577917050117

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