The propagation of axisymmetric waves on the surface of a liquid jet under the action of a radial electric field
is considered. The jet is assumed to be inviscid and perfectly conducting, and a field is set up by placing the jet
concentrically inside a perfectly cylindrical tube whose wall is maintained at a constant potential. A nontrivial
interaction arises between the hydrodynamics and the electric field in the annulus, resulting in the formation
of electrocapillary waves. The main objective of the present study is to describe nonlinear aspects of such
axisymmetric waves in the weakly nonlinear regime, which is valid for long waves relative to the undisturbed
jet radius. This is found to be possible if two conditions hold: the outer electrode radius is not too small, and the
applied electric field is sufficiently strong. Under these conditions long waves are shown to be dispersive and a
weakly nonlinear theory can be developed to describe the evolution of the disturbances. The canonical system
that arises is the Kortweg–de Vries equation with coefficients that vary as the electric field and the electrode
radius are varied. Interestingly, the coefficient of the highest-order third derivative term does not change sign and
remains strictly positive, whereas the coefficient α of the nonlinear term can change sign for certain values of the
parameters. This finding implies that solitary electrocapillary waves are possible; there are waves of elevation
for α > 0 and of depression for α < 0. Regions in parameter space are identified where such waves are found.