Classification of beating solitons, their physical spectra, and second-order nonlinear superpositions

We obtained the full set of multiparameter vector beating soliton solutions for Manakov equations in both focusing and defocusing cases. Based on exact solutions, physical spectra of beating solitons are calculated analytically. It is found that the spectra of moving beating solitons are asymmetric relative to the sign change of the frequency. In contrast, the static beating solitons have symmetric spectra. We also study the second-order vector beating soliton solutions with either equal or unequal velocities. Numerical simulations confirmed the validity of our exact solutions.