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Waves and shocks traveling through the solar chromospheric plasma areinfluenced by its partial ionization and weak collisional coupling, and maybecome susceptible to multi-fluid effects, similar to interstellar shock waves.In this study, we consider fast magneto-acoustic shock wave formation andpropagation in a stratified medium, that is permeated by a horizontal magneticfield, with properties similar to that of the solar chromosphere. The evolutionof plasma and neutrals is modeled using a two-fluid code that evolves a set ofcoupled equations for two separate fluids. We observed that waves in neutralsand plasma, initially coupled at the upper photosphere, become uncoupled athigher heights in the chromosphere. This decoupling can be a consequence ofeither the characteristic spatial scale at the shock front, that becomessimilar to the collisional scale, or the change in the relation between thewave frequency, ion cyclotron frequency, and the collisional frequency withheight. The decoupling height is a sensitive function of the wave frequency,wave amplitude, and the magnetic field strength. We observed that decouplingcauses damping of waves and an increase in the background temperature due tothe frictional heating. The comparison between analytical and numerical resultsallows us to separate the role of the nonlinear effects from the linear ones onthe decoupling and damping of waves.

Two-fluid simulations of waves in the solar chromosphere II. Propagation and damping of fast magneto-acoustic waves and shocks