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 KdVmn equations, is discussed in detail in the paper. The case of KdV23 is given as a paradigmatic example. © 1997 American Institute of Physics.
Casati, P., Falqui, G., Magri, F., & Pedroni, M. (1997). A note on fractional KdV hierarchies. JOURNAL OF MATHEMATICAL PHYSICS, 38(9), 4606-4628 [10.1063/1.532110].
A note on fractional KdV hierarchies
FALQUI, GREGORIO;MAGRI, FRANCO;
1997
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 KdVmn equations, is discussed in detail in the paper. The case of KdV23 is given as a paradigmatic example. © 1997 American Institute of Physics.
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