B. Alvarez-samaniego and D. Lannes, Large time existence for 3D water-waves and asymptotics, Inventiones mathematicae, vol.2, issue.4, pp.165-186, 2009.
DOI : 10.1051/lhb/1953034

URL : https://hal.archives-ouvertes.fr/hal-00281509

R. Beals, D. H. Sattinger, and J. Szmigielski, Multipeakons and the Classical Moment Problem, Advances in Mathematics, vol.154, issue.2, pp.229-257, 2000.
DOI : 10.1006/aima.1999.1883

URL : https://doi.org/10.1006/aima.1999.1883

T. B. Benjamin, The Stability of Solitary Waves, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.328, issue.1573, pp.153-183, 1972.
DOI : 10.1098/rspa.1972.0074

A. Bressan, G. Chen, and Q. Zhang, Uniqueness of conservative solutions to the Camassa- Holm equation via characteristics, Discr. Cont. Dyn. Syst, vol.35, pp.25-42, 2015.

A. Bressan and A. Constantin, Global Conservative Solutions of the Camassa???Holm Equation, Archive for Rational Mechanics and Analysis, vol.27, issue.5, pp.215-239, 2007.
DOI : 10.5802/aif.1757

A. Bressan and A. Constantin, GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA???HOLM EQUATION, Analysis and Applications, vol.455, issue.01, pp.1-27, 2007.
DOI : 10.1081/PDE-120016129

R. Camassa and 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

R. Camassa, D. Holm, and J. Hyman, A New Integrable Shallow Water Equation, Adv. Appl. Mech, p.31, 1994.
DOI : 10.1016/S0065-2156(08)70254-0

A. Constantin, Existence of permanent and breaking waves for a shallow water equation: a geometric approach, Annales de l???institut Fourier, vol.50, issue.2, pp.321-362, 2000.
DOI : 10.5802/aif.1757

A. Constantin, On the scattering problem for the Camassa-Holm equation, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.457, issue.2008, pp.953-970, 2001.
DOI : 10.1098/rspa.2000.0701

A. Constantin and J. Escher, Global existence and blow-up for a shallow water equation, Annali Sc. Norm. Sup. Pisa, vol.26, pp.303-328, 1998.

A. Constantin, V. Gerdjikov, and R. Ivanov, Inverse scattering transform for the Camassa???Holm equation, Inverse Problems, vol.22, issue.6, pp.22-2197, 2006.
DOI : 10.1088/0266-5611/22/6/017

A. Constantin and D. Lannes, The Hydrodynamical Relevance of the Camassa???Holm and Degasperis???Procesi Equations, Archive for Rational Mechanics and Analysis, vol.114, issue.1, pp.165-186, 2009.
DOI : 10.1017/S0308210500024380

URL : https://hal.archives-ouvertes.fr/hal-00281511

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 L. Molinet, Global Weak Solutions for a Shallow Water Equation, Communications in Mathematical Physics, vol.211, issue.1, pp.45-61, 2000.
DOI : 10.1007/s002200050801

A. Constantin and W. Strauss, Stability of peakons, Communications on Pure and Applied Mathematics, vol.363, issue.5, pp.603-610, 2000.
DOI : 10.1007/978-3-7091-2444-4_6

J. Eckhardt and G. , On the isospectral problem of the dispersionless Camassa???Holm equation, Advances in Mathematics, vol.235, pp.469-495, 2013.
DOI : 10.1016/j.aim.2012.12.006

K. Dika and Y. Martel, Stability of $N$ solitary waves for the generalized BBM equations, Dynamics of Partial Differential Equations, vol.1, issue.4, pp.401-437, 2004.
DOI : 10.4310/DPDE.2004.v1.n4.a3

K. Dika and L. Molinet, Stability of multipeakons, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.4, pp.1517-1532, 2009.
DOI : 10.1016/j.anihpc.2009.02.002

URL : https://hal.archives-ouvertes.fr/hal-00260227

K. Dika and L. Molinet, Stability of train of anti-peakons -peakons , Discrete Contin, Dyn. Syst. Ser. B, vol.12, issue.3, pp.561-577, 2009.

M. Grillakis, J. Shatah, and W. Strauss, Stability theory of solitary waves in the presence of symmetry, I, Journal of Functional Analysis, vol.74, issue.1, pp.160-197, 1987.
DOI : 10.1016/0022-1236(87)90044-9

D. Iftimie, Large time behavior in perfect incompressible flows, Partial differential equations and applications, Sémin. Congr, vol.15, pp.119-179, 2007.

R. S. Johnson and . Camassa-holm, Korteweg-de Vries and related models for water waves, J. Fluid Mech, vol.455, pp.63-82, 2002.

B. Kolev, Lie Groups and Mechanics: An Introduction, Journal of Nonlinear Mathematical Physics, vol.21, issue.4, pp.480-498, 2004.
DOI : 10.1007/978-0-387-21792-5

URL : https://hal.archives-ouvertes.fr/hal-00001155

B. Kolev, Poisson brackets in hydrodynamics, Discrete Contin, Dyn. Syst, vol.19, pp.555-574, 2007.
DOI : 10.3934/dcds.2007.19.555

URL : http://www.aimsciences.org/journals/doIpChk.jsp?paperID=2715&mode=full

Y. Martel, F. Merle, and T. , Stability and Asymptotic Stability for Subcritical gKdV Equations, Communications in Mathematical Physics, vol.231, issue.2, pp.347-373, 2002.
DOI : 10.1007/s00220-002-0723-2

Y. Martel and F. Merle, Asymptotic Stability of Solitons??for Subcritical Generalized KdV Equations, Archive for Rational Mechanics and Analysis, vol.157, issue.3, pp.219-254, 2001.
DOI : 10.1007/s002050100138

Y. Martel and F. Merle, Asymptotic stability of solitons of the gKdV equations with general nonlinearity, Mathematische Annalen, vol.39, issue.1, pp.391-427, 2008.
DOI : 10.1353/ajm.2005.0033

URL : https://hal.archives-ouvertes.fr/hal-00678864

L. Molinet and I. Denis-poisson, E-mail address: Luc.Molinet@univ-tours