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Development of perturbations on a weakly inhomogeneous background. (Russian) Zbl 1164.74445
The authors study development of one-dimensional linear growing and damping perturbations on a stationary weakly inhomogeneous background. Main attention is focused on strengthening of the waves arising from the initial perturbations and localized in the domains the length of which is small as compared with the scale of inhomogeneity. A relationship is established between the Hamiltonian method (with complex dispersion equation) and the saddle-point method for asymptotic representation of the integral expressing perturbations via the initial data. Model examples of perturbation developments are considered.

MSC:
74J99 Waves in solid mechanics
74H99 Dynamical problems in solid mechanics
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