The Hunter-Saxton system and the geodesics on a pseudosphere
  We show that the two-component Hunter-Saxton system with negative coupling constant describes the geodesic flow on an infinite-dimensional pseudosphere. This approach yields explicit solution formulae for the Hunter-Saxton system. Using this geometric intuition, we conclude by constructing global weak solutions. The main novelty compared with similar previous studies is that the metric is indefinite. 
Jonatan Lenells and Marcus Wunsch
math.AP math.DG