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The processes of the coronal plasma heating and cooling were previously shownto significantly affect the dynamics of slow magnetoacoustic (MA) waves,causing amplification or attenuation, and also dispersion. However, the entropymode is also excited in such a thermodynamically active plasma and is affectedby the heating/cooling misbalance too. This mode is usually associated with thephenomenon of coronal rain and formation of prominences. Unlike the adiabaticplasmas, the properties and evolution of slow MA and entropy waves incontinuously heated and cooling plasmas get mixed. Different regimes of themisbalance lead to a variety of scenarios for the initial perturbation toevolve. In order to describe properties and evolution of slow MA and entropywaves in various regimes of the misbalance, we obtained an exact analyticalsolution of the linear evolutionary equation. Using the characteristictimescales and the obtained exact solution, we identified regimes withqualitatively different behaviour of slow MA and entropy modes. For some ofthose regimes, the spatio-temporal evolution of the initial Gaussian pulse isshown. In particular, it is shown that slow MA modes may have a range ofnon-propagating harmonics. In this regime, perturbations caused by slow MA andentropy modes in a low-$\beta$ plasma would look identically in observations,as non-propagating disturbances of the plasma density (and temperature) eithergrowing or decaying with time. We also showed that the partition of the initialenergy between slow MA and entropy modes depends on the properties of theheating and cooling processes involved. The obtained exact analytical solutioncould be further applied to the interpretation of observations and results ofnumerical modelling of slow MA waves in the corona and the formation andevolution of coronal rain.

Mixed properties of slow magnetoacoustic and entropy waves in a plasma with heating/cooling misbalance