  In six dimensions there exists a unique one-parameter family of non-linear
conformal electrodynamics for a chiral 2-form gauge field which includes (in a
free-field limit) the linear chiral 2-form theory and is related, by
dimensional reduction, to the four-dimensional ModMax electrodynamics. In this
work, we present the first exact solutions of this theory in presence of
gravity. In particular, we will consider plane-wave, Robinson-Trautman, and
self-dual dyonic string configurations, generalizing well-known solutions of
this type in six-dimensional supergravities with linear chiral 2-form
multiplets.
