The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations
2011 (English)In: Journal of Geometry and Physics, ISSN 0393-0440, Vol. 61, no 2, 436-452 p.Article in journal (Refereed) Published
We use geometric methods to study two natural two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations. We show that these generalizations can be regarded as geodesic equations on the semidirect product of the diffeomorphism group of the circle Diff(S1) with some space of sufficiently smooth functions on the circle. Our goals are to understand the geometric properties of these two-component systems and to prove local well-posedness in various function spaces. Furthermore, we perform some explicit curvature calculations for the two-component Camassa-Holm equation, giving explicit examples of large subspaces of positive curvature. © 2010 Elsevier B.V.
Place, publisher, year, edition, pages
2011. Vol. 61, no 2, 436-452 p.
Camassa-Holm equation, Degasperis-Procesi equation, Geodesic flow, Sectional curvature, Semidirect product
IdentifiersURN: urn:nbn:se:kth:diva-163813DOI: 10.1016/j.geomphys.2010.10.011ISI: 000287283100004ScopusID: 2-s2.0-78349295721OAI: oai:DiVA.org:kth-163813DiVA: diva2:802380
QC 201504132015-04-132015-04-122015-04-13Bibliographically approved