Chin. Phys. B, 2016, Vol. 25(9): 090201    DOI: 10.1088/1674-1056/25/9/090201
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# Localized waves in three-component coupled nonlinear Schrödinger equation

Tao Xu(徐涛), Yong Chen(陈勇)
Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China
Abstract  We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.
Keywords:  localized waves      three-component coupled nonlinear Schrödinger equation      generalized Darboux transformation
Received:  01 April 2016      Revised:  11 May 2016      Accepted manuscript online:
 PACS: 02.30.Ik (Integrable systems) 03.75.Nt (Other Bose-Einstein condensation phenomena) 31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)
Fund: Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).
Corresponding Authors:  Yong Chen     E-mail:  ychen@sei.ecnu.edu.cn