K. M. Berger and P. A. Milewski, Simulation of Wave Interactions and Turbulence in One-Dimensional Water Waves, SIAM Journal on Applied Mathematics, vol.63, issue.4, pp.1121-1140, 2003.
DOI : 10.1137/S0036139902402063

J. L. Bona and M. Chen, A Boussinesq system for two-way propagation of nonlinear dispersive waves, Physica D: Nonlinear Phenomena, vol.116, issue.1-2, pp.191-224, 1998.
DOI : 10.1016/S0167-2789(97)00249-2

J. L. Bona, W. G. Pritchard, and L. R. Scott, Solitary-wave interaction, Physics of Fluids, vol.23, issue.3, pp.438-441, 1980.
DOI : 10.1063/1.863011

J. G. Byatt-smith, The reflection of a solitary wave by a vertical wall, Journal of Fluid Mechanics, vol.15, issue.-1, pp.503-521, 1988.
DOI : 10.1017/S0022112077000081

J. D. Carter and R. Cienfuegos, The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations, European Journal of Mechanics - B/Fluids, vol.30, issue.3, pp.259-268, 2011.
DOI : 10.1016/j.euromechflu.2010.12.002

J. Chambarel, C. Kharif, and J. Touboul, Head-on collision of two solitary waves and residual falling jet formation, Nonlinear Processes in Geophysics, vol.16, issue.1, pp.111-122, 2009.
DOI : 10.5194/npg-16-111-2009

URL : https://hal.archives-ouvertes.fr/hal-00703724

F. Chazel, D. Lannes, and F. Marche, Numerical Simulation of Strongly Nonlinear and Dispersive Waves Using a Green???Naghdi Model, Journal of Scientific Computing, vol.37, issue.3, pp.105-116, 2011.
DOI : 10.1007/s10915-010-9395-9

URL : https://hal.archives-ouvertes.fr/hal-00482561

D. Clamond and D. Dutykh, Practical use of variational principles for modeling water waves, Physica D: Nonlinear Phenomena, vol.241, issue.1, pp.25-36, 2012.
DOI : 10.1016/j.physd.2011.09.015

URL : https://hal.archives-ouvertes.fr/hal-00456891

D. Clamond, M. Francius, J. Grue, and C. Kharif, Long time interaction of envelope solitons and freak wave formations, European Journal of Mechanics - B/Fluids, vol.25, issue.5, pp.536-553, 2006.
DOI : 10.1016/j.euromechflu.2006.02.007

M. J. Cooker, P. D. Weidman, and D. S. Bale, Reflection of a high-amplitude solitary wave at a vertical wall, Journal of Fluid Mechanics, vol.342, issue.5, pp.141-158, 1997.
DOI : 10.1017/S002211209700551X

W. Craig, P. Guyenne, J. Hammack, D. Henderson, and C. Sulem, Solitary water wave interactions, Physics of Fluids, vol.18, issue.5, pp.57106-57110, 2006.
DOI : 10.1063/1.2205916

F. Dias and P. Milewski, On the fully-nonlinear shallow-water generalized Serre equations, Physics Letters A, vol.374, issue.8, pp.1049-1053, 2010.
DOI : 10.1016/j.physleta.2009.12.043

D. Dommermuth, The initialization of nonlinear waves using an adjustment scheme, Wave Motion, vol.32, issue.4, pp.307-317, 2000.
DOI : 10.1016/S0165-2125(00)00047-0

D. Dutykh, D. Clamond, P. Milewski, and D. Mitsotakis, Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations, European Journal of Applied Mathematics, vol.9, issue.05, pp.1-27, 2005.
DOI : 10.1017/S0022112065000745

URL : https://hal.archives-ouvertes.fr/hal-00587994

G. A. El, R. H. Grimshaw, and N. F. Smyth, Unsteady undular bores in fully nonlinear shallow-water theory, Physics of Fluids, vol.18, issue.2, p.27104, 2006.
DOI : 10.1063/1.2175152

J. D. Fenton and M. M. Rienecker, A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions, Journal of Fluid Mechanics, vol.350, issue.-1, pp.411-443, 1982.
DOI : 10.1016/0021-9991(70)90005-7

Y. Goda, Random Seas and Design of Maritime Structures, Advanced Series on Ocean Engineering. World Scientific, vol.33, issue.1, 2010.

A. E. Green, N. Laws, and P. M. Naghdi, On the Theory of Water Waves, Proc. R. Soc. Lond. A, pp.43-55, 1974.
DOI : 10.1098/rspa.1974.0072

A. E. Green and P. M. Naghdi, A derivation of equations for wave propagation in water of variable depth, Journal of Fluid Mechanics, vol.338, issue.02, pp.237-246, 1976.
DOI : 10.1017/S0022112076002425

J. Hammack, D. Henderson, P. Guyenne, and M. Yi, SOLITARY-WAVE COLLISIONS, Advances in Engineering Mechanics ??? Reflections and Outlooks, 2004.
DOI : 10.1142/9789812702128_0013

J. D. Hansom and A. M. Hall, Magnitude and frequency of extra-tropical North Atlantic cyclones: A chronology from cliff-top storm deposits, Quaternary International, vol.195, issue.1-2, pp.42-52, 2009.
DOI : 10.1016/j.quaint.2007.11.010

D. Kelletat, A. G. Comments-to-dawson, and I. Stewart, Tsunami deposits in the geological record, Sedimentary Geology Sedimentary Geology, vol.200, issue.211 10, pp.166-18387, 2007.

D. Lannes and P. Bonneton, Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation, Physics of Fluids, vol.21, issue.1, p.16601, 2009.
DOI : 10.1063/1.3053183

Y. A. Li, Hamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi Equations, Journal of Nonlinear Mathematical Physics, vol.284, issue.sup1, pp.99-105, 2002.
DOI : 10.2991/jnmp.2002.9.s1.9

T. Maxworthy, Experiments on collisions between solitary waves, Journal of Fluid Mechanics, vol.33, issue.01, pp.177-185, 1976.
DOI : 10.1063/1.1666400

C. C. Mei, The applied dynamics of water waves, World Scientific, issue.4, 1989.

N. R. Mirchina and E. Pelinovsky, Increase in the amplitude of a long wave near a vertical wall. Izvestiya, Atmospheric and Oceanic Physics, pp.252-253, 1984.

I. Nikolkina and I. Didenkulova, Rogue waves in 2006???2010, Natural Hazards and Earth System Science, vol.11, issue.11, pp.2913-2924, 2011.
DOI : 10.5194/nhess-11-2913-2011

L. O. 'brien, J. M. Dudley, and F. Dias, Extreme wave events in Ireland, Natural Hazards and Earth System Science, vol.14, issue.133, pp.680-2012625, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00909247

E. N. Pelinovsky, E. Troshina, V. Golinko, N. Osipenko, and N. Petrukhin, Runup of tsunami waves on a vertical wall in a basin of complex topography, Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere, vol.24, issue.5, pp.431-436, 1999.
DOI : 10.1016/S1464-1909(99)00024-6

M. Sainflou, Essai sur les digues maritimes verticales, Annales des Ponts et Chaussées, vol.98, issue.11 1, pp.5-48, 1928.

A. Scheffers, D. Kelletat, S. Haslett, S. Scheffers, and T. Browne, Coastal boulder deposits in Galway Bay and the Aran Islands, western Ireland, Zeitschrift f??r Geomorphologie, Supplementary Issues, vol.54, issue.3, pp.247-279, 2010.
DOI : 10.1127/0372-8854/2010/0054S3-0027

A. Scheffers, S. Scheffers, D. Kelletat, and T. Browne, Wave???Emplaced Coarse Debris and Megaclasts in Ireland and Scotland: Boulder Transport in a High???Energy Littoral Environment, The Journal of Geology, vol.117, issue.5, pp.553-573, 2009.
DOI : 10.1086/600865

F. Serre, ContributionàContributionà l'´ etude desécoulementsdesécoulements permanents et variables dans les canaux, pp.374-388, 1953.

L. F. Shampine, ODE solvers and the method of lines, Numerical Methods for Partial Differential Equations, vol.33, issue.6, pp.739-755, 1994.
DOI : 10.1002/num.1690100608

L. F. Shampine and M. W. Reichelt, The MATLAB ODE Suite, SIAM Journal on Scientific Computing, vol.18, issue.1, pp.1-22, 1997.
DOI : 10.1137/S1064827594276424

URL : https://hal.archives-ouvertes.fr/hal-01333731

J. J. Stoker, Water Waves: The mathematical theory with applications. Interscience, 1957.

C. H. Su and R. M. Mirie, On head-on collisions between two solitary waves, Journal of Fluid Mechanics, vol.46, issue.03, pp.509-525, 1980.
DOI : 10.1103/PhysRevLett.19.1095

M. Tissier, P. Bonneton, F. Marche, F. Chazel, and D. Lannes, Nearshore Dynamics of Tsunami-like Undular Bores using a Fully Nonlinear Boussinesq Model, Journal of Coastal Research, vol.64, pp.603-607, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00799006

G. Wei, J. T. Kirby, S. T. Grilli, and R. Subramanya, A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves, Journal of Fluid Mechanics, vol.107, issue.-1, pp.71-92, 1995.
DOI : 10.1063/1.865459

D. M. Williams, MECHANISMS OF WAVE TRANSPORT OF MEGACLASTS ON ELEVATED CLIFF-TOP PLATFORMS: EXAMPLES FROM WESTERN IRELAND RELEVANT TO THE STORM-WAVE VERSUS TSUNAMI CONTROVERSY, Irish Journal of Earth Sciences, vol.28, issue.-1, pp.13-23, 2010.
DOI : 10.3318/IJES.2010.28.13

N. J. Zabusky and M. D. , Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States, Physical Review Letters, vol.15, issue.6, pp.240-243, 1965.
DOI : 10.1103/PhysRevLett.15.240

M. I. Zheleznyak and E. N. Pelinovsky, Physical and mathematical models of the tsunami climbing a beach, Tsunami Climbing a Beach, pp.8-34, 1985.