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Phenomenological models of essential nonlinear processes in solids with internal structure are developed so as to obtain nonlinear and dispersive features of the material similar to those described by the structural model. The exact solitary wave solutions of the governing equations are used as a tool for a comparison of two kinds of modelling. It is found that the model containing nonlinearity at the microlevel provides maximum similarity with the structural model.

Models for essentially nonlinear strain waves in materials with internal structure