The Hunter-Saxton system and the geodesics on a pseudosphere

Details The Hunter-Saxton system and the geodesics on a pseudosphere The Hunter-Saxton system and the geodesics on a pseudosphere

2012-01-24

arxiv.org/abs/1201.5002v1

Mathematics

Analysis of PDEs

23 pages, 4 figures

Scientific paper

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.

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