Soliton Solutions of the Spin-Orbit Coupled Binary Bose-Einstein Condensate System

In a quantum system with spin, spin-orbit coupling is manifested by linking the spin angular momentum of particle its orbital momentum, which leads to many exotic phenomena. The experimental realization synthetic effects in ultra-cold atomic systems provides an entirely new platform for exploring simulations. spinor Bose-Einstein condensate, can change properties significantly, offers excellent opportunity investigate influence on state at macroscopic level. As typical states effects, solitons coupled condensates be manipulated directly, makes study become one hottest topics research ultracold physics recent years. This paper investigates exact vector soliton solutions Gross-Pitaevskii equation one-dimensional binary condensates, has four parameters <inline-formula><tex-math id="M1">\begin{document}$\mu$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222319_M1.jpg"/><graphic xlink:href="10-20222319_M1.png"/></alternatives></inline-formula>, id="M2">\begin{document}$\delta$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M2.jpg"/><graphic xlink:href="10-20222319_M2.png"/></alternatives></inline-formula>, id="M3">\begin{document}$\alpha$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M3.jpg"/><graphic xlink:href="10-20222319_M3.png"/></alternatives></inline-formula> and id="M4">\begin{document}$\beta$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M4.jpg"/><graphic xlink:href="10-20222319_M4.png"/></alternatives></inline-formula>, where id="M5">\begin{document}$\mu$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M5.jpg"/><graphic xlink:href="10-20222319_M5.png"/></alternatives></inline-formula> denotes strength coupling, id="M6">\begin{document}$\delta$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M6.jpg"/><graphic xlink:href="10-20222319_M6.png"/></alternatives></inline-formula> detuning parameter, id="M7">\begin{document}$\alpha$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M7.jpg"/><graphic xlink:href="10-20222319_M7.png"/></alternatives></inline-formula> id="M8">\begin{document}$\beta$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M8.jpg"/><graphic xlink:href="10-20222319_M8.png"/></alternatives></inline-formula> are self- cross-interaction, respectively. For case id="M9">\begin{document}$\beta=\alpha$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M9.jpg"/><graphic xlink:href="10-20222319_M9.png"/></alternatives></inline-formula>, direct ansatz, two kinds stripe solitons, namely, oscillating dark-dark obtained; meanwhile, transformation presented such that from integrable Manakov system, get equation. id="M10">\begin{document}$\beta=3\alpha$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M10.jpg"/><graphic xlink:href="10-20222319_M10.png"/></alternatives></inline-formula>, bright-W type id="M11">\begin{document}$\alpha>0$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M11.jpg"/><graphic xlink:href="10-20222319_M11.png"/></alternatives></inline-formula> kink-antikink id="M12">\begin{document}$\alpha<0$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M12.jpg"/><graphic xlink:href="10-20222319_M12.png"/></alternatives></inline-formula> presented. It found relation between id="M13">\begin{document}$\mu$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M13.jpg"/><graphic xlink:href="10-20222319_M13.png"/></alternatives></inline-formula> id="M14">\begin{document}$\delta$\end{document}</tex-math><alternatives><graphic xlink:href="10-20222319_M14.jpg"/><graphic xlink:href="10-20222319_M14.png"/></alternatives></inline-formula> affect solitons. Based these solutions, corresponding dynamics impact magnetization spin-polarized domains discussed. Our results show result rich two-component Bose gases, including as well classical non-stripe various multi-solitons. Furthermore, remarkable behaviors magnetization. experiments there have been different methods observe population distribution, magnetic domains, so our provide some possible options related experiments.