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A well-known mathematical model representing a chain of oscillators consisting of elastic elements and masses, each of which contains an internal oscillator and describing the class of acoustic metamaterials "mass-in-mass", is generalized by taking into account the nonlinearity of the external and (or) internal elastic elements. As a result of analysis of the long-wavelength approximation of the obtained system, it is shown that spatially localized nonlinear deformation waves (solitons) can be formed in a metamaterial, under dynamic influence on it. The dependencies connecting the parameters of a localized wave are determined: amplitude, velocity and width with inertial and elastic characteristics of the metamaterial.

LOCALIZED NON-LINEAR WAVES OF DEFORMATION IN THE CLASS OF METAMATERIALS AS AS A CHAIN OF "MASS-V-MASS"