  Biadjoint scalar field theory has been the subject of much recent study, due
to a number of applications in field and string theory. The catalogue of exact
non-linear solutions of this theory is relatively unexplored, despite having a
role to play in extending known relationships between gauge and gravity
theories, such as the double copy. In this paper, we present new solutions of
biadjoint scalar theory, corresponding to singular line configurations in four
spacetime dimensions, with a power-law dependence on the cylindrical radius.
For a certain choice of common gauge group (SU(2)), a family of infinitely
degenerate solutions is found, whose existence can be traced to the global
symmetry of the theory. We also present extended solutions, in which the pure
power-law divergence is partially screened by a form factor.
