The Hunter-Saxton system and the geodesics on a pseudosphere
Jonatan Lenells, Marcus Wunsch
TL;DR
This paper links the two-component Hunter-Saxton system with negative coupling to geodesic flow on an infinite-dimensional pseudosphere, providing explicit solutions and constructing global weak solutions through a geometric perspective.
Contribution
It introduces a novel geometric interpretation of the Hunter-Saxton system involving an indefinite metric, leading to explicit solutions and global weak solutions.
Findings
Explicit solution formulas for the Hunter-Saxton system
Geometric interpretation as geodesic flow on a pseudosphere
Construction of global weak solutions
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Algebraic structures and combinatorial models