Ukrainian Journal of Physical Optics

2024 Volume 25, Issue 5

ISSN 1609-1833 (Print)


1Xuzhen Gao, 2Jincheng Shi, 3Milivoj R. Belic, 4Junbo Chen, 5Jiawei Li, 6,7Liangwei Zeng and 6Xing Zhu

1Department of Physics, Lyuliang University, Lishi, Shanxi 033001, China
254th Research Institute of CETC, Sh?iazhuang 050011, China,
3Division of Arts and Sciences, Texas A&M University at Qatar, 23874 Doha, Qatar
4School of Physics and Electronic Engineering, Jiaying University, Meizhou 514015, China
5Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China
6Department of Basic Courses, Guangzhou Maritime University, Guangzhou 510725, China
7College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China


We demonstrate W-shaped solitons sustained under the inhomogeneous self-defocusing Kerr nonlinearity in the nonlinear Schrӧdinger equation. These solitons are dark or gray beams that ride on a constant background. We obtain different types of W-shaped solitons when the parameters in the equation are set suitably. All W-shaped solitons found are stable, established by the linear stability analysis, and checked by direct numerical simulation. Power defect arising in these soliton families is also investigated, and we find that the power defect change with the propagation constant is nearly linear. Besides standard perturbed propagation, we also display propagation with modulated parameters and find that the sudden variation of the appropriate parameter leads to unacceptable distortions and instability in the solution, while the gradual change of the parameter restores regular stable behavior.

Keywords: W-shaped solitons, Kerr nonlinearity, self-defocusing, Schrodinger equation

UDC: 535.32

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    Отримано розв’язки для W-подібних солітонів, які є стійкими за умови неоднорідної самодефокусуючої нелінійності Керра в нелинійному рівнянні Шредингера. Ці солітони є темними або сірими пучками, які поширюються на постійному фоні. Отриманя різні типи W-подібних солітонів, при певному встановленні параметрів рівняння. Усі W-подібні солітони є стійкими, що підтверджено лінійним аналізом стійкості, а також перевірено за допомогою прямого чисельного моделювання. Досліджено також дефект потужності, що виникає у цьому сімействі солітонів, і виявлено, що зміна дефекту потужності з константою поширення є майже лінійна. Крім стандартного поширення, продемонстровано можливість поширення з модульованими параметрами і виявлено, що раптова зміна відповідного параметра призводить до неприйнятних спотворень і нестійкості у рішенні, тоді як поступова зміна цього ж параметра відновлює стійку поведінку.

    Ключові слова: W-подібні солітони, керрівська нелінійність, само-дефокусування, рівняння Шредінгера

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