Two generalisations of the Evans function, for the analysis of the linearis
ation about solitary waves, are shown to be equivalent. The generalisation
introduced by Alexander, Gardner and Jones [J. reine Angew. Math. 410 (1990
) 167] is based on exterior algebra and the generalisation introduced by Sw
inton [Phys. Lett. A 163 (1992) 57] is based on a matrix formulation and ad
joint systems. In regions of the complex plane where both formulations are
defined, the equivalence is geometric: we show that the formulations are du
al and the duality can be made explicit using Hedge duality and the Hedge s
tar operator. Swinton's formulation excludes potential branch points at whi
ch the Alexander, Gardner and Jones formulation is well-defined. Therefore
we consider the implications of equivalence on the analytic continuation of
the two formulations. (C) 1999 Published by Elsevier Science B.V.