Multi-solitons in the spin-orbit-coupled spin-1 Bose-Einstein condensates

We find a restrictive integrable reduction for the one-dimensional spin-orbit-coupled spin-1 Bose-Einstein condensate system, which allows us to reduce the three-component Gross-Pitaevskii system into the two-component Manakov system or the single cubic Schrödinger equation. Based on the reduction, we obtain the multi-breathers, higher-order rouge waves and multi-dark soliton solutions for ferromagnetic and anti-ferromagnetic system, respectively. Furthermore, the impacts of the spin-orbit coupling to the multi-soliton dynamics, and the stability of these soliton solutions have also been discussed