Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates

摘要

We find one-, two-, and three-component solitons of the polar andferromagnetic (FM) types in the general (non-integrable) model of a spinor(three-component) model of the Bose-Einstein condensate (BEC), based on asystem of three nonlinearly coupled Gross-Pitaevskii equations. The stabilityof the solitons is studied by means of direct simulations, and, in a part,analytically, using linearized equations for small perturbations. Globalstability of the solitons is considered by means of the energy comparison. As aresult, ground-state and metastable soliton states of the FM and polar typesare identified. For the special integrable version of the model, we develop theDarboux transformation (DT). As an application of the DT, analytical solutionsare obtained that display full nonlinear evolution of the modulationalinstability (MI) of a continuous-wave (CW) state seeded by a small spatiallyperiodic perturbation. Additionally, by dint of direct simulations, wedemonstrate that solitons of both the polar and FM types, found in theintegrable system, are structurally stable, i.e., they are robust under randomchanges of the relevant nonlinear coefficient in time.