so old as the quasiparticle approach itself is.
They
are well known, for example, in the theory of metals where many attempts have
been made to  derive a complete system of dynamic equations, consisting of
equations from the theory of elasticity, a kinetic equation for the electron
gas and Maxwell's
equations (cf. Refs. \cite{KontUFN,Kontbook}
 and the bibliography cited there).
\par
The attempts to deduce the equations of motion for a quasiparticle in
$L$-system can be divided into two groups corresponding to
 the twofold role of the
dispersion law. In the co-moving frame it coincides with both energy and
Hamiltonian. Therefore transformations typical of energy and Hamilton function
have been proved.
\par
    When considering $\eps({\bf k},u_{ik})$ as Hamiltonian a transformation
by a substitutional function of the form
\begin{equation}
\tilde \Phi({\bf r', p }, t) = ({\bf r' + u}({\bf r'}, t)){\bf p}
\ee
has been used and the following relations have been obtained
(see e.g. \cite{KontUFN,Kontbook}):
$$
{\bf k = p} + \frac{\p}{\p {\bf r'}}({\bf u p}),
\tilde H({\bf p,r}, t) =
\tilde \eps ({\bf k, r'},t) + {\bf \dot u p},
$$
where $\bf r = r' + u $ are the coordinates in $L$-system and $\, \bf p\,$
is 