  We present a new family of exact solutions of the Einstein equations,
constructed through the Khan-Penrose procedure, that may be interpreted as
representing the propagation of a pair of solitons, in the background of a
plane-wave collision spacetime. The metric in the interaction region is
obtained as a diagonal solitonic perturbation of Rindler's spacetime, applying
the Belinskii and Zakharov Inverse Scattering Method (ISM), with two real poles
and a pair of complex conjugate poles. We use a non-standard renormalization
procedure, obtaining solutions that contain two more parameters than in the
standard ISM. We analyze the asymptotic behaviour of the solutions in the limit
where the determinant of the Killing part of the metric vanishes, finding in
this limit a curvature singularity, except when the free parameters contained
in the solutions satisfy a particular relation. Assuming this condition is
satisfied, we show that the metric is regular in the above mentioned limit, and
that the spacetimes contain in this case a Killing Cauchy horizon instead of a
curvature singularity. The solutions are analytically extended through the
horizon, and we find a curvature singularity in this extension, related to the
presence and propagation of the complex poles.
