  The analysis of the system behavior under the effect of the additive noises
has been done using a simple model of shear melting. The situation with low
intensity of the order parameter noise has been investigated in detail, and
time dependence of the order parameter has been calculated. A distinctive
feature of the obtained dependence is power-law distribution and
self-similarity. The generalized Hurst exponent of the time series has been
found within multifractal detrended fluctuation analysis. It is shown that the
self-similarity of the time series increases when the noise intensity reduces.
