Dynamics of the Manakov-typed bound vector solitons with random initial perturbations

Dynamics of the bound vector solitons with random initial perturbations is investigated for the Manakov model, which describes the propagation of the multimode soliton pulses in nonlinear fiber optics and two-component matter-wave solitons in the quasi-one-dimensional Bose-Einstein condensates (BECs) without confining potential. We review the analytic two-bound-vector-soliton solutions and give the three-bound-vector-soliton solutions. Breakup of the typical bound state is presented numerically when the symmetry and asymmetry random perturbations are added to the initial conditions. Relationship between the lifetime of the bound state and amplitude of the random perturbation is discussed. Meanwhile, existence of the symmetry-recovering is illustrated for the bound vector solitons with the asymmetry random perturbations. Discussions of this paper could be expected to be helpful in interpreting the dynamics of the Manakov-typed bound vector solitons when the random initial noises in nonlinear optical fibers or stochastic quantum fluctuations in the BECs are considered.