Physics Commons^™

Unification Of Ernst-Equation Backlund Transformations Using A Modified Wahlquist-Estabrook Technique; Wahlquist-Estabrook, B. Kent Harrison

Faculty Publications

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.