Vector solitons for the (2 + 1)-dimensional coupled nonlinear Schrödinger system in the Kerr nonlinear optical fiber,ZAMM - Journal of Applied Mathematics and Mechanics

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Vector solitons for the (2 + 1)-dimensional coupled nonlinear Schrödinger system in the Kerr nonlinear optical fiber
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-05-12 , DOI: 10.1002/zamm.202000232
Yan Sun _{1,

2} , Bo Tian _{1,

2} , Qi‐Xing Qu ₃ , Han‐Peng Chai _{1,

2} , Yu‐Qiang Yuan _{1,

2} , Wen‐Rui Shan _{1,

2} , Yan Jiang _{1,

2}

Affiliation

Investigated in this paper is the (2 + 1)-dimensional coupled nonlinear Schrödinger system, which describes the propagation of the optical soliton through the Kerr nonlinear fiber in which each component diffracts in two transverse dimensions. By virtue of the Kadomtsev-Petviashvili hierarchy reduction, we obtain the bright, dark and mixed vector soliton solutions in terms of the Gramian. We investigate the vector solitons graphically: (1) Bright-dark one solitons with one of the components being gray or black are shown. Bouncing, beating, oscillating and breathing effects which appear during the interactions between the bright-dark two solitons are discussed, and those interactions are shape-preserving; (2) Degenerate and non-degenerate dark-dark one solitons are presented. Interaction of the dark-dark two solitons is discussed and the two solitons keep their amplitudes and velocities invariant except for some phase shifts during the interaction; (3) Bound-state and complexes of the bright-bright solitons are presented.

中文翻译：

克尔非线性光纤中 (2 + 1) 维耦合非线性薛定谔系统的矢量孤子

本文研究的是 (2 + 1) 维耦合非线性薛定谔系统，它描述了光孤子通过克尔非线性光纤的传播，其中每个分量在两个横向维度上衍射。凭借 Kadomtsev-Petviashvili 层级约简，我们根据 Gramian 获得了亮、暗和混合矢量孤子解。我们以图形方式研究矢量孤子：（1）显示了具有灰色或黑色分量之一的亮暗孤子。讨论了明暗两个孤子相互作用过程中出现的弹跳、跳动、振荡和呼吸效应，这些相互作用是保形的；(2) 提出简并和非简并暗暗孤子。讨论了暗暗两个孤子的相互作用，两个孤子在相互作用过程中除了一些相移外，保持幅度和速度不变；(3) 给出了亮亮孤子的束缚态和复合体。

更新日期：2021-05-12

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