Burgers and Kadomtsev-Petviashvili hierarchies: A functional representation approach
- Cite this article as:
- Dimakis, A. & Müller-Hoissen, F. Theor Math Phys (2007) 152: 933. doi:10.1007/s11232-007-0079-z
Functional representations of (matrix) Burgers and potential Kadomtsev-Petviashvili (pKP) hierarchies (and others), as well as some corresponding Bäcklund transformations, can be obtained surprisingly simply from a “discrete” functional zero-curvature equation. We use these representations to 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.