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Vector rogue waves in the mixed coupled nonlinear Schrödinger equations

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Abstract.

In this paper, via the generalized Darboux transformation we derive the reduced and non-reduced vector rogue wave solutions of the focusing-defocusing mixed coupled nonlinear Schrödinger equations. The dynamics of reduced vector rogue waves is the same as that for the known scalar ones. The non-reduced solutions can exhibit both the one-peak-two-valleys structure with one peak and two valleys lying in a straight line, and the two-peaks-two-valleys structure with two peaks and two valleys located at the four vertices of a parallelogram. We also find that the amplitude of the non-reduced vector rogue wave is not three times as that of the exciting plane wave, and that the coalescence of multiple fundamental rogue waves does not generate larger-amplitude rogue waves. In addition, we discuss the relationship of the free parameters in the solutions with the positions and relative distances of rogue waves in the xt-plane.

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Authors and Affiliations

  1. Department of Mathematics and Physics, North China Electric Power University, 102206, Beijing, China

    Min Li

  2. College of Science, China University of Petroleum, 102249, Beijing, China

    Huan Liang, Tao Xu & Changjing Liu

Authors
  1. Min Li
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  2. Huan Liang
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  3. Tao Xu
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  4. Changjing Liu
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Corresponding author

Correspondence to Tao Xu.

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Li, M., Liang, H., Xu, T. et al. Vector rogue waves in the mixed coupled nonlinear Schrödinger equations. Eur. Phys. J. Plus 131, 100 (2016). https://doi.org/10.1140/epjp/i2016-16100-1

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  • DOI: https://doi.org/10.1140/epjp/i2016-16100-1

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