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Chin. Phys. B, 2024, Vol. 33(9): 090207    DOI: 10.1088/1674-1056/ad6258
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Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions

Luyao Zhang(张路瑶) and Xiyang Xie(解西阳)†
Department of Mathematics and Physics, Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China
Abstract  We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrödinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses on the dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions under non-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole or double-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and the spatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons, we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions. In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle” crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one and two dark solitons.
Keywords:  double-pole solitons      double-pole breathers      Riemann-Hilbert problem      non-zero boundary conditions      nonlinear Schrödinger equation with sextic operator  
Received:  27 June 2024      Revised:  07 July 2024      Accepted manuscript online:  12 July 2024
PACS:  02.30.Ik (Integrable systems)  
  02.30.Rz (Integral equations)  
  42.81.Dp (Propagation, scattering, and losses; solitons)  
Fund: Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 2024MS126).
Corresponding Authors:  Xiyang Xie     E-mail:  xiyangxie@ncepu.edu.cn

Cite this article: 

Luyao Zhang(张路瑶) and Xiyang Xie(解西阳) Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions 2024 Chin. Phys. B 33 090207

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