The hunter-saxton equation: A geometric approach
2008 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 40, no 1, 266-277 p.Article in journal (Refereed) Published
We provide a rigorous foundation for the geometric interpretation of the Hunter-Saxton equation as the equation describing the geodesic flow of the H 1 right-invariant metric on the quotient space Rot(double-struck S)\D k(double-struck S) of the infinite-dimensional Banach manifold D k(double-struck S) of orientationpreserving H k- diffeomorphisms of the unit circle double-struck S modulo the subgroup of rotations Rot(double-struck S). Once the underlying Riemannian structure has been established, the method of characteristics is used to derive explicit formulas for the geodesies corresponding to the H 1 right-invariant metric, yielding, in particular, new explicit expressions for the spatially periodic solutions of the initial-value problem for the Hunter-Saxton equation.
Place, publisher, year, edition, pages
2008. Vol. 40, no 1, 266-277 p.
Diffeomorphism group, Geodesic flow, Hunter-saxton equation, Diffeomorphisms, Explicit expressions, Explicit formulas, Geometric approaches, Geometric interpretations, Method of characteristics, Periodic solutions, Quotient spaces, Riemannian structures, Unit circles, Banach spaces, Initial value problems, Geodesy
Physical Sciences Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-163827DOI: 10.1137/050647451ISI: 000256453200011ScopusID: 2-s2.0-61849127242OAI: oai:DiVA.org:kth-163827DiVA: diva2:802366
QC 201504272015-04-122015-04-122015-04-27Bibliographically approved