Varied Branches of Nondegenerate Vector Solitons

TL;DR

This paper explores the complex structure and stability of nondegenerate vector solitons in multi-component Manakov systems, revealing multiple stable branches with unique dispersion relations and extending findings to N-component models.

Contribution

It introduces the existence of multiple stable nondegenerate vector soliton branches and their dispersion relations in multi-component systems, a novel insight into soliton diversity.

Findings

Four distinct branches of nondegenerate dark-bright-bright solitons identified.

All soliton branches are stable against weak perturbations.

Extension to N-component systems shows exponential growth in soliton branches.

Abstract

Our study on nondegenerate dark-bright-bright solitons in a three-component Manakov model with repulsive interactions reveals the existence of diverse branches of nondegenerate vector solitons. For fixed bright component particle numbers and a given soliton velocity, the nondegenerate dark-bright-bright solitons exhibit four distinct branches with different density profiles and phase distributions, comprising two positive mass branches and two negative mass branches. The energy-velocity dispersion relation of each pair of positive- and one negative-mass branches form a closed loop, resulting in two mutually independent loops for the soliton's overall dispersion. All soliton branches share a common maximal velocity, which is determined by the larger bright soliton particle number. Linear stability analysis shows that all these branches are stable against weak perturbations. Extending to an $N$-component Manakov system, the nondegenerate solitons have $2^{N-1}$ distinct branches, of which $2^{N-2}$ branches solitons is positive mass and $2^{N-2}$ branches solitons is negative mass. Each pair of positive- and negative-mass branches form a closed dispersion relation loop, so that the vector solitons have $2^{N-2}$ disjoint loops. These results uncover the rich branches and interesting dispersion relations of nondegenerate vector solitons in multi-component models.