Magnon dispersions in quantum Heisenberg ferrimagnetic chains at zero temperature

Within the Dyson-Maleev boson formalism, we study the zero-temperature magn on dispersions in a family of one-dimensional quantum Heisenberg ferrimagne ts 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 fo r the low-energy excitations. The spin-stiffness constant rho(s) and the op tical magnon gap Delta of different (S-1,S-2) ferrimagnetic systems are cal culated, respectively, to second and third order in the quasiparticle inter action. The spin-wave results are compared with available numerical estimat es.