Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics

doi:10.1088/1674-1056/26/12/120201

中国物理B ›› 2017, Vol. 26 ›› Issue (12): 120201-120201.doi: 10.1088/1674-1056/26/12/120201

• GENERAL • 下一篇

Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics

Tao Xu(徐涛), Yong Chen(陈勇), Ji Lin(林机)

1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;
2. Department of Physics, Zhejiang Normal University, Jinhua 321004, China;
3. MOE International Joint Laboratory of Trustworthy Software, East China Normal University, Shanghai 200062, China

收稿日期:2017-07-05 修回日期:2017-08-12 出版日期:2017-12-05 发布日期:2017-12-05
通讯作者: Yong Chen E-mail:ychen@sei.ecnu.edu.cn
基金资助:
Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11675054 and 11435005), the Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213), and the Natural Science Foundation of Hebei Province, China (Grant No. A2014210140).

Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics

Tao Xu(徐涛)^1,3, Yong Chen(陈勇)^1,2,3, Ji Lin(林机)²

1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;
2. Department of Physics, Zhejiang Normal University, Jinhua 321004, China;
3. MOE International Joint Laboratory of Trustworthy Software, East China Normal University, Shanghai 200062, China

Received:2017-07-05 Revised:2017-08-12 Online:2017-12-05 Published:2017-12-05
Contact: Yong Chen E-mail:ychen@sei.ecnu.edu.cn
Supported by:
Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11675054 and 11435005), the Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213), and the Natural Science Foundation of Hebei Province, China (Grant No. A2014210140).

摘要/Abstract

摘要： We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrödinger (CCQNLS) equations through the generalized Darboux transformation (DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higher-order localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed:(i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; (ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; (iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.

关键词: generalized Darboux transformation, localized waves, soliton, rogue wave, breather, coupled cubic-quintic nonlinear Schrö, dinger equations

Abstract: We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrödinger (CCQNLS) equations through the generalized Darboux transformation (DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higher-order localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed:(i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; (ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; (iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.

Key words: generalized Darboux transformation, localized waves, soliton, rogue wave, breather, coupled cubic-quintic nonlinear Schrö, dinger equations

中图分类号: (Integrable systems)

02.30.Ik

03.75.Nt (Other Bose-Einstein condensation phenomena) 31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)

徐涛, 陈勇, 林机. Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics[J]. 中国物理B, 2017, 26(12): 120201-120201.

Tao Xu(徐涛), Yong Chen(陈勇), Ji Lin(林机). Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics[J]. Chin. Phys. B, 2017, 26(12): 120201-120201.

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Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics

Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics

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