**The International Conference on
**

Secondary Calculus and Cohomological Physics,

Moscow, August 24 - August 31, 1997

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Symmetries of equations containing a small parameter

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Alexey V. Samokhin

Diffiety Institute (Russia) and Moscow State University of Civil Aviation 20 Kronshtadtsky Blvd., Moscow 125838, Russia E-mail: asamokhin@glasnet.ru

**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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