RESUMEN
Parametric coupling of waves is one of the most efficient mechanisms of energy transfer that can lead to the growth or decay of waves. This transfer occurs at frequencies close to their natural frequencies. In partially ionized solar plasma, there are a multitude of waves that can undergo this process. Here, we study the parametric coupling of Alfvén waves propagating in a partially ionized solar plasma with ionization-recombination waves identified by our study to appear in a plasma in ionization non-equilibrium. Depending on the parameters that describe the plasma (density, temperature), coupling can lead to a parametric resonance. Our study determines the occurrence conditions of parametric resonance, by finding the boundaries between stable and unstable regions in the parameter space. Our results show that collisions and non-equilibrium recombination can both contribute to the onset of unstable behaviour of parametrically resonant Alfvén waves. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.