KdV shock-like waves as invariant solutions of KdV equation symmetries

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We consider the following hypothesis: some of KdV equation shock-like waves are invariant with respect to the combination of the Galilean symmetry and KdV equation higher symmetries. Also we demonstrate our approach on the example of Burgers equation.
7 pages, LaTEX, version 2.09, submitted to Phys. Lett. A

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