Ukrainian Journal of Physical Optics

2024 Volume 25, Issue 5

ISSN 1609-1833 (Print)

Bright and Dark Solitons in a (2+1)-Dimensional Spin-1 Bose-Einstein Condensates

1Nan Li, 1Quan Chen, 2Houria Triki, 3Feiyan Liu, 1,3Yunzhou Sun, 4Siliu Xu and 3Qin Zhou

1Hubei Province Engineering Research Center for Intelligent Micro-Nano Medical Equipment and Key Technologies, School of Electronic and Electrical Engineering, Wuhan Textile University, Wuhan 430200, China,
2Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P.O. Box 12, 23000 Annaba, Algeria
3Research Center of Nonlinear Science, School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan 430200, China,
4School of Biomedical Engineering and Medical Imaging, Xianning Medical College, Hubei University of Science and Technology, Xianning 437100, China


The three-coupled Gross-Pitaevskii equation with a harmonic potential in a (2+1)-dimensional spin-1 Bose-Einstein condensate is studied in this paper. Using the Hirota bilinear method, the bright and dark soliton solutions of the system with attractive and repulsive interactions are obtained, and the amplitudes and velocities of those solitons are also given. In addition, we analyze the influence of harmonic potential on the dynamics of solitons and discuss the interaction between solitons through asymptotic analysis. As a result, we find that the amplitude and velocity of solitons are related to the harmonic potential, and the interaction between the two solitons is elastic.

Keywords: soliton, Hirota bilinear method, asymptotic analysis, Bose-Einstein condensates

UDC: 535.32

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    У цій статті досліджується тризв’язане рівняння Гросса-Пітаєвського з гармонічним потенціалом у (2+1)-вимірному бозе-ейнштейнівському конденсаті зі спіном-1. За допомогою білінійного методу Хіроти отримано світлі та темні солітонні розв’язки системи з взаємодіями притягання та відштовхування, а також наведено амплітуди та швидкості цих солітонів. Крім того, проаналізовано вплив гармонічного потенціалу на динаміку солітонів і досліджується взаємодія між солітонами за допомогою асимптотичного аналізу. У результаті виявлено, що амплітуда і швидкість солітонів пов’язані з гармонічним потенціалом, а взаємодія між двома солітонами є пружною.

    Ключові слова: солітон, білінійний метод Хірота, асимптотичний аналіз, конденсат Бозе-Ейнштейна

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