An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described. Application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model. 02.90.+p; 11.10.Hi

Plastic deformation at constant rate and low temperatures starting with 20–30K, as a rule, occurs in the form of oscillations of the deforming stress (serrated deformation). Low-temperature serrated deformation (LTSD) appears under special conditions where deformation occurs as a result of the specific conditions of dislocation dynamics and, possibly, as result of special physical conditions of deformation (low thermal conductivity and specific heat of the sample, heat exchange with the cooling medium). A large number of experimental and theoretical works have been performed since the discovery of LTSD in the 1950s but not even one review has appeared. Further advances in understanding the mechanism of LTSD and the development of a theory of this phenomenon require that the experimental data be systematized. As a rule, individual experimental facts have been used when theories of LTSD have been compared with experiment. The present review attempts to collect as much accessible experimental data as possible, systematize these data, determine the main characteristics of LTSD, examine theoretical hypotheses, compare theory with experiment, and suggest possible mechanisms for low-temperature serrated deformation.

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