Asymptotic behavior of the thermal vibrations of a deformed crystal lattice

Asymptotic behaviour in the unit cell parameter of the dynamical equations for atomic displacements in $a$ crystal lattice with given external long-wave deformation is investigated. The equations obtained in the long-wave limit reduce to the equations of the elasticity theory with variable coefficients. The explicit form of asymptotic solution is written out and two cases of the external deformation, homogeneous and plane running wave, are considered in detail.