  The role of the spin-phonon coupling in spin-Peierls chains doped with spin-0
or spin-1 impurities is investigated by various numerical methods such as exact
diagonalization, quantum Monte Carlo simulations and Density Matrix
Renormalization Group. Various treatments of the lattice, in a fully quantum
mechanical way, classically in the adiabatic approximation or using a fixed
three-dimensional dimerization pattern are compared. For an isolated chain,
strong bonds form between the two spin-1/2 sites next to the impurity site,
leading to the appearance of magneto-elastic solitons. We also show that these
excitations do not bind to spin-0 impurities but are weakly attracted by spin-1
impurities. However, the interchain elastic coupling generates an effective
confining potential at the non-magnetic impurity site which can lead to the
formation of soliton-impurity bound states. We also predict that a soliton and
an antisoliton bound to two impurities on the same chain can annihilate each
other when the separation between the impurities is smaller than a critical
value depending on the interchain elastic constant.
