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    Varied dispersion relation branches of nondegenerate vector solitons

    Yu-Hao Wang1, Liang Duan1, Yan-Hong Qin2, and Li-Chen Zhao1,3,4,5,*

    • 1School of Physics, Northwest University, Xi'an 710127, China
    • 2School of Physical Science and Technology, Xinjiang University, Urumqi 830046, China
    • 3NSFC-SPTP Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China
    • 4Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
    • 5Fundamental Discipline Research Center for Quantum Science and Technology of Shaanxi Province, Xi'an 710127, China

    • *Contact author: zhaolichen3@nwu.edu.cn

    Phys. Rev. E 114, 024217 – Published 19 August, 2026

    DOI: https://doi.org/10.1103/czq6-jvy9

    Abstract

    We systematically investigate the dispersion relations of nondegenerate dark-bright-bright solitons in a three-component Manakov model with repulsive interactions. We show that the vector solitons possess four distinct dispersion relation branches, comprising two positive-mass branches and two negative-mass branches. The energy-velocity dispersion relation of each pair of positive- and negative-mass branches forms a closed loop, resulting in two disjoint loops for the soliton's overall dispersion. All soliton branches share a common maximum speed (much lower than the sound speed), at which branch degeneracies emerge. The maximum speed is determined by the larger bright soliton particle number for the nondegenerate dark-bright-bright soliton, in contrast to the partially degenerate case. Linear stability analysis shows that all these branches are stable against weak perturbations. Extending these results to the four-component Manakov model yields eight distinct nondegenerate soliton branches. Combining these results, we conclude that for an N-component Manakov system, the nondegenerate solitons have 2N−1 distinct branches, of which half are positive-mass branches and the other half are negative-mass branches. Each pair of positive- and negative-mass branches forms a closed dispersion relation loop, so that the vector solitons have 2N−2 disjoint loops. These results reveal rich degeneracy structures in soliton dispersion relations and may motivate experiments on externally driven vector-soliton dynamics.

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