Kouranbaeva, Shinar The Camassa-Holm equation as a geodesic flow on the diffeomorphism group. (English) Zbl 0958.37060 J. Math. Phys. 40, No. 2, 857-868 (1999). The paper deals with a physically meaningful generalization of the Camassa-Holm (CH) equation to higher dimension. In particular it is shown that the (CH) equation is the geodesic flow of the weak Riemannian metric on the diffeomorphism group of the line or the circle obtained by right translating in \(H^1\). Reviewer: Messoud Efendiev (Berlin) Cited in 129 Documents MSC: 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds 86A05 Hydrology, hydrography, oceanography Keywords:Camassa-Holm equation; weak Riemannian metric; entire group PDF BibTeX XML Cite \textit{S. Kouranbaeva}, J. Math. Phys. 40, No. 2, 857--868 (1999; Zbl 0958.37060) Full Text: DOI arXiv References: [1] DOI: 10.1103/PhysRevLett.71.1661 · Zbl 0972.35521 [2] DOI: 10.1016/S0065-2156(08)70254-0 [3] DOI: 10.2307/1970699 · Zbl 0211.57401 [4] DOI: 10.1017/S030821050002477X · Zbl 0795.58018 [5] DOI: 10.1006/aima.1998.1721 · Zbl 0951.37020 [6] DOI: 10.1006/jfan.1998.3335 · Zbl 0933.58010 [7] DOI: 10.5802/aif.233 · Zbl 0148.45301 [8] DOI: 10.1016/S0393-0440(97)00010-7 · Zbl 0901.58022 [9] DOI: 10.1007/BF00739423 · Zbl 0808.35124 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.