  We study magnon-magnon interactions and their effects in a spiral magnet
induced by combination of an antiferromagnetic Heisenberg interaction and a
Dzyaloshinsky-Moriya interaction. We show that the main effect of magnon-magnon
interactions on low-energy magnons is to renormalize the coefficient of energy
dispersion. This could explain why some experiments are consistent with the
noninteracting theory. We also show that although the magnon-magnon
interactions induce the pair amplitude for low-energy magnons, its effect on
the excitation energy is negligible. This suggests that for magnons the finite
pair amplitude does not necessarily accompany the pair condensation.
