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For systems of evolutionary partial differential equations the tau-structureis an important notion which originated from the deep relation betweenintegrable systems and quantum field theories. We show that, under a certainnon-degeneracy condition, existence of a tau-structure implies integrability.As an example, we apply this principle to provide a new proof of theintegrability of the Drinfeld--Sokolov hierarchy associated to an arbitraryKac--Moody algebra and a choice of a vertex of its Dynkin diagram.

Remarks on intersection numbers and integrable hierarchies. II. Tau-structure