k})$ of a quasiparticle are well defined only in an ideal periodic lattice. In such a lattice the dispersion law as well as all other physical quantities are periodic functions in the reciprocal space ($ k$-space). However, in any real system the crystal lattice is deformed (e.g. by impurities, elastic deformations, external fields etc.). The most complicated problems concern the quasiparticle dynamics in a time-varying deformed crystal lattice. In an exact description all physical characteristics of a quasiparticle have to be periodic functions of the quasimomentum with periods which are functions of the coordinates and the time. This leads to a dependence of the Brillouin zone boundaries not only on the deformation at a given instant, but also on the local lattice velocity [@Push; @AP].

As for the stationary (or quasistationary) case, this difficulty has usually been passed over by introducing a local dispersion law $\eps({\bf k}, u_{ik})$ and further expansion in powers of the small deformation tensor components $u_{ik}$: $$\eps({\bf k}, u_{ik}) = \eps_0({\bf k}) + \lambda_{ik}({\bf k})u_{ik}
\ee          %1
where $\lambda_{ik}$ are the deformation potential components,
\begin{equation}
u_{ik}({\bf r}) = \frac {1}{2}\left( \frac{\partial u_i}{\partial x_k} +
\f{\p x_i}{\p x_k} \right),
\ee            %2
and $\bf u$ is the deformation 