  Within the Dyson-Maleev boson formalism, we study the zero-temperature magnon
dispersions in a family of one-dimensional quantum Heisenberg ferrimagnets
composed of two different spins $(S_1,S_2)$ in the elementary cell. It is shown
that the spin-wave theory can produce precise quantitative results for the
low-energy excitations. The spin-stiffness constant $\rho_s$ and the optical
magnon gap $\Delta$ of different $(S_1,S_2)$ ferrimagnetic systems are
calculated, respectively, to second and third order in the quasiparticle
interaction. The spin-wave results are compared with available numerical
estimates.
