Riemann-Liouville integrals of fractional order and extended KP hierarchy

Details Riemann-Liouville integrals of fractional order and extended KP hierarchy Riemann-Liouville integrals of fractional order and extended KP hierarchy

2002-07-21

arxiv.org/abs/nlin/0207037v1

J.Phys.A35:9657-9670,2002

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, Latex with iopart

Scientific paper

10.1088/0305-4470/35/45/312

An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/N-th order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding out the new extensions of the KP hierarchy, brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional order pseudo-differential operators.

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