Soliton, rational and special solutions of the Korteweg-de Vries hierarchy

Soliton, rational and special solutions for any member of the Korteweg-de Vries hierarchy are presented. It is shown that the soliton solutions are found by means of the Hirota formulae with change of the dispersion relation, special solutions for the Korteweg-de Vries hierarchy are expressed via the transcendents of the first and the second Painlevé hierarchies and rational solutions of members for the Korteveg-de Vries hierarchy can be presented using the Yablonski-Vorobév polynomials.