Varied dispersion relation branches of nondegenerate vector solitons

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 2^{N-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 2^{N-2} disjoint loops. These results reveal rich degeneracy structures in soliton dispersion relations and may motivate experiments on externally driven vector-soliton dynamics.