Abstract
One of the cornerstones of the theory of integrable systems of KdV type has been the remark that the n-GD (Gel’fand–Dickey) equations are reductions of the full Kadomtsev–Petviashvilij (KP) theory. In this paper we address the analogous problem for the fractional KdV theories, by suggesting candidates of the “KP theories” lying behind them. These equations are called “KP(m) hierarchies,” and are obtained as reductions of a bigger dynamical system, which we call the “central system.” The procedure allowing passage from the central system to the KP(m) equations, and then to the fractional KdVnm equations, is discussed in detail in the paper. The case of KdV32 is given as a paradigmatic example.
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