Burgers and KP hierarchies: A functional representation approach

Details Burgers and KP hierarchies: A functional representation approach Burgers and KP hierarchies: A functional representation approach

2006-10-19

arxiv.org/abs/nlin/0610045v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages

Scientific paper

10.1007/s11232-007-0079-z

From a 'discrete' functional zero curvature equation, functional representations of (matrix) Burgers and potential KP (pKP) hierarchies (and others), as well as corresponding Backlund transformations, can be obtained in a surprisingly simple way. With their help we show that any solution of a Burgers hierarchy is also a solution of the pKP hierarchy. Moreover, the pKP hierarchy can be expressed in the form of an inhomogeneous Burgers hierarchy. In particular, this leads to an extension of the Cole-Hopf transformation to the pKP hierarchy. Furthermore, these hierarchies are solved by the solutions of certain functional Riccati equations.

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