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Interactions of localized wave structures and dynamics in the defocusing coupled nonlinear Schrödinger equations

Guoqiang Zhang1,2, Zhenya Yan1,2,*, Xiao-Yong Wen1,3, and Yong Chen1,2

  • 1Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
  • 2School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • 3Department of Mathematics, School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

  • *zyyan@mmrc.iss.ac.cn
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Phys. Rev. E 95, 042201 – Published 10 April, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.042201

Abstract

We investigate the defocusing coupled nonlinear Schrödinger equations from a 3×3 Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.

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Phys. Rev. E 95, 042201– Published 10 April, 2017
  • Received 25 November 2016

©2017 American Physical Society

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