Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions

doi:10.1088/1674-1056/ad6258

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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Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions

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