The Hunter-Saxton system and the geodesics on a pseudosphere

2012/01/24 by Jonatan Lenells, Marcus Wunsch, Lenells, Jonatan +1
Mathematics · Physics and Astronomy · #35B44 (Secondary) #35D30 #53C21 #53C22 (Primary) #53C50 #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #math.DG #msc:35B44 #msc:35D30 #msc:53C21 #msc:53C22 #msc:53C50

paper · pdf · doi:10.48550/arxiv.1201.5002

23 pages, 4 figures

arxiv created 2012/01/24 · openalex publication_date 2012/01/24 · arxiv updated 2012/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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