2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147547Polaronic effects are investigated in the two dimensional t--J model (describing Cu spins and holes of the planes in high-$T_c$ cuprates) in the presence of in-plane dynamic oxygen breathing modes. We focus on the effect of dynamic multi-phonon modes. Spin and charge structure factors are computed. We found evidence for self-localisation of the holes and {\it increased} short range antiferromagnetic spin-spin correlations between the remaining spins. This effect persists when all the in-plane oxygen vibration degrees of freedom are taken into account. This suggests that dynamic phonons could play a key role in stabilizing inhomogeneous stripe phases or domain wall structures.Revised version, RevTex, 3 pages, 3 figures in uuencoded format appendedCondensed Mattertext