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<p>The Gell-Mann Matrices produced by the SU(3) group can better describe the direct coupling between the three internal states of atoms in spin-1 system, which is distinct from the traditional SU(2) group. This paper investigates approximately exact bright-dark solitons in the SU(3) spin-orbit coupled spin-1 Bose-Einstein condensate (BEC) system using the multiple-scale expansion method. It provides a detailed analysis of the influence of SU(3) spin-orbit coupling parameters on soliton characteristics, including amplitude, propagation velocity, and phase. The asymptotic analysis method confirms the elastic collision properties between solitons and reveals that these solitons exhibit both ferromagnetic and biaxial nematic states. Finally, the Deep Operator Network (DeepONet) approach is employed to validate bright/dark solitons. These findings in the SU(3) spin-orbit coupled BEC system offer a foundational theoretical perspective to study emergent nonlinear transport behaviors in condensed matter physics.</p>

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Asymptotic approximate solitons with ferromagnetic and biaxial nematic states in spin-1 Bose-Einstein condensates with SU(3) spin-orbit coupling

  • 期刊论文

  • 发表日期：

    2026年1月13日

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  • Hua-Tao Liu,
  • Fei-Yan Liu,
  • Houria Triki,
  • Qin Zhou

摘要

The Gell-Mann Matrices produced by the SU(3) group can better describe the direct coupling between the three internal states of atoms in spin-1 system, which is distinct from the traditional SU(2) group. This paper investigates approximately exact bright-dark solitons in the SU(3) spin-orbit coupled spin-1 Bose-Einstein condensate (BEC) system using the multiple-scale expansion method. It provides a detailed analysis of the influence of SU(3) spin-orbit coupling parameters on soliton characteristics, including amplitude, propagation velocity, and phase. The asymptotic analysis method confirms the elastic collision properties between solitons and reveals that these solitons exhibit both ferromagnetic and biaxial nematic states. Finally, the Deep Operator Network (DeepONet) approach is employed to validate bright/dark solitons. These findings in the SU(3) spin-orbit coupled BEC system offer a foundational theoretical perspective to study emergent nonlinear transport behaviors in condensed matter physics.