Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation

doi:10.1088/1674-1056/26/10/100204

中国物理B ›› 2017, Vol. 26 ›› Issue (10): 100204-100204.doi: 10.1088/1674-1056/26/10/100204

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

收稿日期:2017-08-04 修回日期:2017-08-14 出版日期:2017-10-05 发布日期:2017-10-05
通讯作者: Zuo-Nong Zhu E-mail:znzhu@sjtu.edu.cn
基金资助:
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)).

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

Received:2017-08-04 Revised:2017-08-14 Online:2017-10-05 Published:2017-10-05
Contact: Zuo-Nong Zhu E-mail:znzhu@sjtu.edu.cn
Supported by:
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)).

摘要/Abstract

摘要： 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.

关键词: multi-component NLS-Boussinesq equation, soliton solution, rogue wave solution

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.

Key words: multi-component NLS-Boussinesq equation, soliton solution, rogue wave solution

中图分类号: (Integrable systems)

02.30.Ik

04.20.Jb (Exact solutions) 04.30.Nk (Wave propagation and interactions) 05.45.Yv (Solitons)

宋彩芹, 肖冬梅, 朱佐农. Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation[J]. 中国物理B, 2017, 26(10): 100204-100204.

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[J]. Chin. Phys. B, 2017, 26(10): 100204-100204.

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Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation

Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation

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