  To calculate linear oscillations and waves in dynamics of gas and plasma one
uses as a rule the old classical method of dispersion equation for complex
frequencies $\omega$ and wave numbers $k$: $\epsilon(\omega,k)=0$. This method
appears to be inapplicable, f.e., in the case of waves in Maxwellian
collisionless plasma when dispersion equation has no solutions. By means of
some refined sophistication L.~Landau in 1946 has suggested in this case
actually to replace the dispersion equation with another one, having a specific
solution (``Landau damping'') and being now widely used in plasma physics.
Recently we have suggested a quite new universal method of two-dimensional
Laplace transformation (in coordinate $x$ and time $t$ for plane wave case),
that allows to obtain asymptotical solutions of original Vlasov plasma
equations as inseparable sets of coupled oscillatory modes (but not a single
wave like $\exp(-i\omega t+i k x)$). The mode parameters are defined in this
case by double-poles ($\omega_n$,$k_n$) of Laplace image $E(\omega_n,k_n)$ of
electrical field $E(x,t)$. This method allows one to obtain the whole set of
oscillatory modes for every concrete problem. It leads to some new ideology in
the theory of plasma oscillations, which are considered as a combination of
coupled oscillatory modes (characterized by pairs ($\omega_n$,$k_n$) and
amplitudes) and depend not only on the intrinsic plasma parameters, but also on
mutually dependent self-consistent initial and boundary conditions and on
method of plasma oscillations excitation.
