  We derive an effective Hamiltonian that takes into account the quantum nature
of phonons and models cooperative Jahn-Teller effect in the adiabatic regime
and at strong electron-phonon coupling in one dimension. Our approach involves
mapping a strong-coupling problem to a weak-coupling one by using a duality
transformation. Subsequently, a sixth-order perturbation theory is employed in
the polaronic frame of reference where the small parameter is inversely
(directly) proportional to the coupling (adiabaticity). We study charge and
orbital order in ferromagnetic manganite chains and address the pronounced
electron-hole asymmetry in the observed phase diagram. In particular, at strong
coupling, we offer an explanation for the observed density dependence of the
wavevector of charge modulation, i.e., wavevector is proportional to
(independent of) electron density on the electron-doped (hole-doped) side of
the phase diagram of manganites. We also provide a picture for the charge and
orbital order at special fillings $ \frac{1}{2}$, $\frac{1}{3}$, $\frac{1}{4}$,
and $ \frac{1}{5}$; while focusing on the ordering controversy at fillings
$\frac{1}{3}$ and $\frac{1}{4}$, we find that Wigner-crystal arrangement is
preferred over bi-stripe order.
