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The localized plastic deformation and the law-like regularities underlying its development in solids are considered. The characteristic features of localized plasticity are analyzed for a wide range of materials. Thus a correlation is established between the products of scales and of process rates obtained for the elastic and plastic deformation. It is a favorable ground for hypothesizing causal links between the elastic and plastic deformation by introducing an elastic-plastic invariant, which is the master equation of the autowave plasticity model being developed. Localized plasticity phenomena are proposed to be addressed in the frame of autowave and quasi-particle approach.