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Burgers and KP hierarchies: A functional representation approach | | Aristophanes Dimakis
; Folkert Muller-Hoissen
; | | Date: |
19 Oct 2006 | | Subject: | Exactly Solvable and Integrable Systems | | Abstract: | 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. | | Source: | arXiv, nlin/0610045 | | Services: | Forum | Review | PDF | Favorites | |
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