Diffiety Institute (Russia) and Moscow State University of Civil Aviation 20 Kronshtadtsky Blvd., Moscow 125838, Russia E-mail: email@example.com
Abstract: For differential equations containing a small parameter $\epsilon$ symmetries are found in a form of series in powers of $\e$. The recurrent relation on summands of the series is obtained; the first summand is just a symmetry of the unperturbed equation (i.e., for an equation with $\e=0$). Conservation laws of the unperturbed equation are not conserved in case $\e\neq 0$ and the rate of their decay is explicitly determined. Illustrative examples include the Burgers equation and a system of magnetohydrodynamics equations.
Keywords: Symmetry, conservation law, differential equation, small parameter
Classification (MSC91): 58G35 35Q53 35A30
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