Abstract
It is well known that the self-similar solutions of the Korteweg-de Vries equation and the modified Korteweg-de Vries equation are expressed via the solutions of the first and second Painleve equations. In this paper we solve this problem for all equations from the Korteveg-de Vries, modified Korteweg-de Vries, Kaup-Kupershmidt, Caudrey-Dodd-Gibbon and Fordy-Gibbons hierarchies. We show that the self-similar solutions of equations corresponding to hierarchies mentioned above can be found by means of the general solutions of higher-order Painleve hierarchies introduced more than ten years ago.
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