Generally Solitary Waves in Model of Pre-deformed Nonlinear Composite

Localized waves are considered in a model of the elastic composite being in the predeformed state. It is shown that in contrast to the case of a composite without previous deformations, classical solitary waves (solitons) under consideration - solutions, branching out of the zero solution (quiescent state), are replaced by generally solitary waves which result from the soliton’s nonlinear resonance and finite-period wave. It is also shown that the availability of generally solitary waves brings to the dispersion decay of localized disturbances due to the resonance wave radiation.