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Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms
University of Cambridge, United Kingdom .ORCID iD: 0000-0001-6191-7769
2008 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 342, no 3, 617-656 p.Article in journal (Refereed) Published
Abstract [en]

We study an equation lying 'mid-way' between the periodic Hunter-Saxton and Camassa-Holm equations, and which describes evolution of rotators in liquid crystals with external magnetic field and self-interaction. We prove that it is an Euler equation on the diffeomorphism group of the circle corresponding to a natural right-invariant Sobolev metric. We show that the equation is bihamiltonian and admits both cusped and smooth traveling-wave solutions which are natural candidates for solitons. We also prove that it is locally well-posed and establish results on the lifespan of its solutions. Throughout the paper we argue that despite similarities to the KdV, CH and HS equations, the new equation manifests several distinctive features that set it apart from the other three.

Place, publisher, year, edition, pages
2008. Vol. 342, no 3, 617-656 p.
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Mathematics
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URN: urn:nbn:se:kth:diva-163828DOI: 10.1007/s00208-008-0250-3ISI: 000258718300008Scopus ID: 2-s2.0-50849122333OAI: oai:DiVA.org:kth-163828DiVA: diva2:802363
Note

QC 20150416

Available from: 2015-04-12 Created: 2015-04-12 Last updated: 2017-12-04Bibliographically approved

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Lenells, Jonatan

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