R. Bishop and B. Neill, Manifolds of negative curvature, Transactions of the American Mathematical Society, vol.145, issue.11, pp.1-49
DOI : 10.1090/S0002-9947-1969-0251664-4

R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solitons, Physical Review Letters, vol.337, issue.11, pp.1661-1664, 1993.
DOI : 10.1098/rsta.1991.0133

URL : http://arxiv.org/pdf/patt-sol/9305002

A. Constantin and B. Kolev, Geodesic flow on the diffeomorphism group of the circle, Commentarii Mathematici Helvetici, vol.78, issue.4, pp.787-804, 2003.
DOI : 10.1007/s00014-003-0785-6

URL : https://hal.archives-ouvertes.fr/hal-00003261

A. Constantin and D. Lannes, The hydrodynamical relevance of the Camassa?Holm and degasperis?procesi equations. Archive for Rational Mechanics and Analysis, pp.165-186, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00170213

H. H. Dai, Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod, Acta Mechanica, vol.5, issue.1-4, pp.193-207, 1998.
DOI : 10.1007/BF01170373

G. David, J. Ebin, and . Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math, vol.92, issue.2, pp.102-163, 1970.

L. Eisenhart, Dynamical Trajectories and Geodesics, The Annals of Mathematics, vol.30, issue.1/4, pp.591-606, 1928.
DOI : 10.2307/1968307

T. Gallouët and F. Vialard, The Camassa???Holm equation as an incompressible Euler equation: A geometric point of view, Journal of Differential Equations, vol.264, issue.7, pp.4199-4234, 2018.
DOI : 10.1016/j.jde.2017.12.008

D. D. Holm, J. E. Marsden, and T. S. Ratiu, The Euler???Poincar?? Equations and Semidirect Products with Applications to Continuum Theories, Advances in Mathematics, vol.137, issue.1, pp.1-81, 1998.
DOI : 10.1006/aima.1998.1721

D. Darryl, J. E. Holm, and . Marsden, Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation, The breadth of symplectic and Poisson geometry, pp.203-235, 2005.

B. Khesin, J. Lenells, G. Misiolek, and S. C. Preston, Geometry of diffeomorphism groups, complete integrability and optimal transport. ArXiv e-prints, 2011.

B. Khesin, G. Misiolek, and K. Modin, Geometric Hydrodynamics via Madelung Transform. ArXiv e-prints, 2017.

S. Kouranbaeva, The Camassa???Holm equation as a geodesic flow on the diffeomorphism group, Journal of Mathematical Physics, vol.40, issue.2, pp.857-868, 1999.
DOI : 10.1007/BF00739423

W. Peter, D. Michor, and . Mumford, Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms, Doc. Math, vol.10, pp.217-245, 2005.

W. Peter, D. Michor, and . Mumford, On Euler's equation and 'EPDiff, J. Geom. Mech, vol.5, issue.3, pp.319-344, 2013.

L. Molinet, On Well-Posedness Results for Camassa-Holm Equation on the Line: A Survey, Journal of Nonlinear Mathematical Physics, vol.27, issue.4, pp.521-533, 2004.
DOI : 10.1081/PDE-120016129

J. Peter, P. Olver, and . Rosenau, Tri-hamiltonian duality between solitons and solitary-wave solutions having compact support, Phys. Rev. E, vol.53, pp.1900-1906, 1996.

C. Stephen and . Preston, The geometry of barotropic flow, Journal of Mathematical Fluid Mechanics, vol.15, issue.4, pp.807-821, 2013.

T. Tao, On the universality of the incompressible Euler equation on compact manifolds. ArXiv e-prints, 2017.