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This article is cited in 11 scientific papers (total in 11 papers)
Burgers and Kadomtsev–Petviashvili hierarchies: A functional
representation approach
A. Dimakisa, F. Müller-Hoissenb a University of the Aegean
b Max Planck Institute for Dynamics and Self-Organization
Abstract:
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.
Keywords:
Burgers hierarchy, Cole–Hopf transformation, Kadomtsev–Petviashvili hierarchy, functional Riccati equation.
Citation:
A. Dimakis, F. Müller-Hoissen, “Burgers and Kadomtsev–Petviashvili hierarchies: A functional
representation approach”, TMF, 152:1 (2007), 66–82; Theoret. and Math. Phys., 152:1 (2007), 933–947
Linking options:
https://www.mathnet.ru/eng/tmf6071https://doi.org/10.4213/tmf6071 https://www.mathnet.ru/eng/tmf/v152/i1/p66
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Abstract page: | 476 | Full-text PDF : | 238 | References: | 43 | First page: | 1 |
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