TOPICAL REVIEW: On the geometric approach to the motion of inertial mechanical systems

By Adrian Constantin, Boris Kolev. 2002

212 citations recorded by the source corpus.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d6daef3d6b81863f16c7db630bb3aa6cb11be621

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Citations in the corpus

On Well-Posedness Results for Camassa-Holm Equation on the Line: A Survey (2004, background): “Finally, (C-H) is also a re-expression of geodesic flow on the diffeomorphism group of the line, see [26], [10], [11].”
THE GEOMETRY OF THE TWO-COMPONENT CAMASSA-HOLM AND DEGASPERIS-PROCESI EQUATIONS (2010, background): “.e. the topology induced by the metric is weaker than the natural topology of any tangent space) and therefore the metric does not establish an isomorphism between the tangent space and its dual, cf. [5, 8, 21]. It is a ﬁrst aim of this section to establish that ∇ as deﬁned in (3.3) deﬁnes a smooth ”
Conservation laws of the Camassa–Holm equation (2005, background): “Equation (1.1) is a re-expression of the geodesic ﬂow in the group of compressible diffeomorphisms of the circle [19, 9, 10] and an inﬁnite-dimensional completely integrable Hamiltonian system [1, 3, 5, 11, 16].”
A Note on the Degasperis-Procesi Equation (2005, background): “2) is a re-expression of geodesic flow on the group of diffeomorphisms of the line [20] (see also [4, 6, 7]) whereas (1.”
On geodesic exponential maps of the Virasoro group (2007, background): “According to [10], this is not true for k = 0.”
Blow-up of solutions to the DGH equation (2007, unknown): “[13].”
Traveling wave solutions of the Camassa-Holm equation (2005, background): “1) satisfies the least action principle[17]: a state of the system is transformed to another nearby state through a uniquely determined flow that minimizes the energy (see also [18]).”
Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View (2007, methodology): “In Constantin and Kolev (2002), the Camassa– Holm equation is derived as a geodesic equation on the group of diffeomorphism equipped with a right-invariant metric.”
Low-Regularity Solutions of the Periodic Camassa–Holm Equation (2007, methodology): “However, the notion of (uniform) well-posedness used in the example of Himonas and Misiolek (2000) (cf. also Constantin and Kolev, 2002) is unusually strong.”
Geodesic flow on the diffeomorphism group of the circle (2003, unknown): “Proposition 1 [7].”