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We consider spin-1 Haldane chains with single-ion anisotropy, which exists inknown Haldane chain materials. We develop a perturbation theory in terms ofanisotropy, where magnon-magnon interaction is important even in the lowtemperature limit. The exact two-particle form factor in the O(3) nonlinearsigma model leads to quantitative predictions on several dynamical propertiesincluding dynamical structure factor and electron spin resonance frequencyshift. These agree very well with numerical results, and with experimental dataon the Haldane chain material Ni(C$_5$H$_{14}$N$_2$)$_2$N$_3$(PF$_6$).

Single-ion anisotropy in Haldane chains and form factor of the O(3) nonlinear sigma model