The Hunter-Saxton system and the geodesics on a pseudosphere
Analysis of PDEs
2012-01-25 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.1201.5002,
title = {The Hunter-Saxton system and the geodesics on a pseudosphere},
author = {Jonatan Lenells and Marcus Wunsch},
journal= {arXiv preprint arXiv:1201.5002},
year = {2012}
}
Comments
23 pages, 4 figures