Backlund transformations, Ernst equation, Wahlquist-Estabrook technique
The three known Backlund transformations for the Ernst equation are derived using a modification of the Wahlquist-Estabrook prolongation procedure. The modification requires that the equation to be studied be cast into a set of differential forms and their exterior derivatives, such that all coefficients are constant (a "CC ideal''). Analysis of the resulting equations produces 16 solutions composed of the three basic transformations combined with identity and other essentially trivial transformations. The group structure of the transformations is discussed. A Backlund transformation (already known) for the Ernst-Maxwell equations can be found by the same method. Promising generalizations are mentioned.
Original Publication Citation
Harrison, Kent B. "Unification of Ernst-equation Backlund transformations using a modified Wahlquist-Estabrook technique." Journal of Mathematical Physics 24 (1983): 2178-2187.
BYU ScholarsArchive Citation
Harrison, B. Kent, "Unification of Ernst-equation Backlund transformations using a modified Wahlquist-Estabrook technique; Wahlquist-Estabrook" (1983). All Faculty Publications. 758.
Physical and Mathematical Sciences
Physics and Astronomy
© 1983 American Institue of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics and may be found at http://link.aip.org/link/?JMAPAQ/24/2178/1
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