Slow magnetoacoustic waves are omnipresent in both natural and laboratory plasma systems. The wave-induced misbalance between plasma cooling and heating processes causes the amplification or attenuation, and also dispersion, of slow magnetoacoustic waves. The wave dispersion could be attributed to the presence of characteristic time scales in the system, connected with the plasma heating or cooling due to the competition of the heating and cooling processes in the vicinity of the thermal equilibrium. We analysed linear slow magnetoacoustic waves in a plasma in a thermal equilibrium formed by a balance of optically thin radiative losses, field-align thermal conduction, and an unspecified heating. The dispersion is manifested by the dependence of the effective adiabatic index of the wave on the wave frequency, making the phase and group speeds frequency-dependent. The mutual effect of the wave amplification and dispersion is shown to result into the occurrence of an oscillatory pattern in an initially broadband slow wave, with the characteristic period determined by the thermal misbalance time scales, i.e. by the derivatives of the combined radiation loss and heating function with respect to the density and temperature, evaluated at the equilibrium. This effect is illustrated by estimating the characteristic period of the oscillatory pattern, appearing because of thermal misbalance in the plasma of the solar corona. It is found that by an order of magnitude the period is about the typical periods of slow magnetoacoustic oscillations detected in the corona.

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The isentropic thermal instability of media with a generalized heat-loss function and negative bulk viscosity condition are discussed. We obtain the nonlinear equation taking into account the nonlinear saturation of the isentropic instability. This equation describes the nonstationary evolution of acoustical waves in media with the isentropic instability. Its stationary solutions are investigated analytically. The most interesting solution is the self-sustained pulse. Using the numerical simulation of the nonlinear acoustical equation and the full system of one-dimensional nonstationary hydrodynamical equations, we showed the disintegration of the initial weak perturbation of compression into sequence of these self-sustained pulses in low-density PDRs.