中国物理B ›› 2019, Vol. 28 ›› Issue (12): 120201-120201.doi: 10.1088/1674-1056/ab50fc

• GENERAL •    下一篇

Dark and multi-dark solitons in the three-component nonlinear Schrödinger equations on the general nonzero background

Zhi-Jin Xiong(熊志进), Qing Xu(许庆), Liming Ling(凌黎明)   

  1. 1 School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China;
    2 School of Mathematics, South China University of Technology, Guangzhou 510640, China
  • 收稿日期:2019-08-29 修回日期:2019-10-09 出版日期:2019-12-05 发布日期:2019-12-05
  • 通讯作者: Liming Ling E-mail:linglm@scut.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11771151), the Guangdong Natural Science Foundation of China (Grant No. 2017A030313008), the Guangzhou Science and Technology Program of China (Grant No. 201904010362), and the Fundamental Research Funds for the Central Universities of China (Grant No. 2019MS110).

Dark and multi-dark solitons in the three-component nonlinear Schrödinger equations on the general nonzero background

Zhi-Jin Xiong(熊志进)1, Qing Xu(许庆)2, Liming Ling(凌黎明)2   

  1. 1 School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China;
    2 School of Mathematics, South China University of Technology, Guangzhou 510640, China
  • Received:2019-08-29 Revised:2019-10-09 Online:2019-12-05 Published:2019-12-05
  • Contact: Liming Ling E-mail:linglm@scut.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11771151), the Guangdong Natural Science Foundation of China (Grant No. 2017A030313008), the Guangzhou Science and Technology Program of China (Grant No. 201904010362), and the Fundamental Research Funds for the Central Universities of China (Grant No. 2019MS110).

摘要: We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrödinger equation. As the plane wave background undergoes unitary transformation SU(3), we obtain the general nonzero background and study its modulational instability by the linear stability analysis. On the basis of this background, we study the dynamics of one-dark soliton and two-dark-soliton phenomena, which are different from the dark solitons studied before. Furthermore, we use the numerical method for checking the stability of the one-dark-soliton solution. These results further enrich the content in nonlinear Schrödinger systems, and require more in-depth studies in the future.

关键词: dark soliton, three-component nonlinear Schrödinger equations, general nonzero background

Abstract: We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrödinger equation. As the plane wave background undergoes unitary transformation SU(3), we obtain the general nonzero background and study its modulational instability by the linear stability analysis. On the basis of this background, we study the dynamics of one-dark soliton and two-dark-soliton phenomena, which are different from the dark solitons studied before. Furthermore, we use the numerical method for checking the stability of the one-dark-soliton solution. These results further enrich the content in nonlinear Schrödinger systems, and require more in-depth studies in the future.

Key words: dark soliton, three-component nonlinear Schrödinger equations, general nonzero background

中图分类号:  (Integrable systems)

  • 02.30.Ik
03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations) 42.81.Dp (Propagation, scattering, and losses; solitons)