  The multi-fluid modelling of high-frequency waves in partially ionized
plasmas has shown that the behavior of magnetohydrodynamics waves in the linear
regime is heavily influenced by the collisional interaction between the
different species that form the plasma. Here, we go beyond linear theory and
study large-amplitude waves in partially ionized plasmas using a nonlinear
multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfv\'en
waves generate density and pressure perturbations. Those nonlinear effects are
more pronounced for standing oscillations than for propagating waves. By means
of numerical simulations and analytical approximations, we examine how the
collisional interaction between ions and neutrals affects the nonlinear
evolution. The friction due to collisions dissipates a fraction of the wave
energy, which is transformed into heat and consequently rises the temperature
of the plasma. As an application, we investigate frictional heating in a plasma
with physical conditions akin to those in a solar quiescent prominence.
