I'm happy to announce the publication of a paper in collaboration with Samuel Crew (Lincoln College, Oxford). In this paper, we revisit the classic problem of a periodic wave travelling without change of form, which was first considered by Stokes in the late 19th century.
Interestingly, there are still several unanswered questions regarding this canonical example of a water wave. Some of these questions concern the existence of the singularities in the complex plane, along with their behaviour as the wave steepens. You can read the paper here.