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Chin. Phys. B, 2017, Vol. 26(10): 100204    DOI: 10.1088/1674-1056/26/10/100204
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Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation

Cai-Qin Song(宋彩芹), Dong-Mei Xiao(肖冬梅), Zuo-Nong Zhu(朱佐农)
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Abstract  The nonlinear Schrödinger (NLS) equation and Boussinesq equation are two very important integrable equations. They have widely physical applications. In this paper, we investigate a nonlinear system, which is the two-component NLS equation coupled to the Boussinesq equation. We obtain the bright-bright, bright-dark, and dark-dark soliton solutions to the nonlinear system. We discuss the collision between two solitons. We observe that the collision of bright-bright soliton is inelastic and two solitons oscillating periodically can happen in the two parallel-traveling bright-bright or bright-dark soliton solution. The general breather and rogue wave solutions are also given. Our results show again that there are more abundant dynamical properties for multi-component nonlinear systems.
Keywords:  multi-component NLS-Boussinesq equation      soliton solution      rogue wave solution  
Received:  04 August 2017      Revised:  14 August 2017      Published:  05 October 2017
PACS:  02.30.Ik (Integrable systems)  
  04.20.Jb (Exact solutions)  
  04.30.Nk (Wave propagation and interactions)  
  05.45.Yv (Solitons)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11371248, 11431008, 11271254, 11428102, and 11671255) and the Fund from the Ministry of Economy and Competitiveness of Spain (Grant Nos. MTM2012-37070 and MTM2016-80276-P (AEI/FEDER,EU)).
Corresponding Authors:  Zuo-Nong Zhu     E-mail:  znzhu@sjtu.edu.cn

Cite this article: 

Cai-Qin Song(宋彩芹), Dong-Mei Xiao(肖冬梅), Zuo-Nong Zhu(朱佐农) Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation 2017 Chin. Phys. B 26 100204

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