  Magnetoacoustic oscillations are nowadays routinely observed in various
regions of the solar corona. This allows them to be used as means of diagnosing
plasma parameters and processes occurring in it. Plasma diagnostics, in turn,
requires a sufficiently reliable MHD model to describe the wave evolution. In
our paper, we focus on obtaining the exact analytical solution to the problem
of the linear evolution of standing slow magnetoacoustic (MA) waves in coronal
loops. Our consideration of the properties of slow waves is conducted using the
infinite magnetic field assumption. The main contribution to the wave dynamics
in this assumption comes from such processes as thermal conduction, unspecified
coronal heating, and optically thin radiation cooling. In our consideration,
the wave periods are assumed to be short enough so that the thermal misbalance
has a weak effect on them. Thus, the main non-adiabatic process affecting the
wave dynamics remains thermal conduction. The exact solution of the
evolutionary equation is obtained using the Fourier method. This means that it
is possible to trace the evolution of any harmonic of the initial perturbation,
regardless of whether it belongs to entropy or slow mode. We show that the
fraction of energy between entropy and slow mode is defined by the thermal
conduction and coronal loop parameters. It is shown for which parameters of
coronal loops it is reasonable to associate the full solution with a slow wave,
and when it is necessary to take into account the entropy wave. Furthermore, we
obtain the relationships for the phase shifts of various plasma parameters
applicable to any values of harmonic number and thermal condition coefficient.
In particular, it is shown that the phase shifts between density and
temperature perturbations for the second harmonic of the slow wave vary between
$\pi/2$ to 0, but are larger than for the fundamental harmonic.

Solar and Stellar Astrophysics;Plasma Physics