The International Conference on
Secondary Calculus and Cohomological Physics,
Moscow, August 24 - August 31, 1997

Symmetries of equations containing a small parameter

Alexey V. Samokhin

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

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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