We report on density-matrix renormalization-group and analytical work on S=
1 antiferromagnetic Heisenberg spin chains. We study the finite-size behavi
or within the framework of the nonlinear sigma model. We study the effect o
f magnon-magnon interactions on the finite-size spectrum and on the magneti
zation curve close to the critical magnetic field, determine the magnon sca
ttering length, and compare it to the prediction from the nonlinear sigma m
odel.