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  • Berger, K. M., and P. A. Milewski (2003), Simulation of wave interactions and turbulence in one-dimensional water waves, SIAM J. Appl. Math.,63(4), 11211140.
  • Bona, J. L., and M. Chen (1998), A Boussinesq system for two-way propagation of nonlinear dispersive waves, Physica D, 116, 191224.
  • Bona, J. L., W. G. Pritchard, and L. R. Scott (1980), Solitary-wave interaction, Phys. Fluids, 23, 438441.
  • Byatt-Smith, J. G. B. (1988), The reflection of a solitary wave by a vertical wall, J. Fluid Mech., 197, 503521.
  • Carter, J. D., and R. Cienfuegos (2011), The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations, Eur. J. Mech. B Fluids, 30, 259268.
  • Chambarel, J., C. Kharif, and J. Touboul (2009), Head-on collision of two solitary waves and residual falling jet formation, Nonlinear Processes Geophys., 16, 111122.
  • Chazel, F., D. Lannes, and F. Marche (2011), Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model, J. Sci. Comput., 48, 105116.
  • Clamond, D., and D. Dutykh (2012), Practical use of variational principles for modeling water waves, Physica D, 241(1), 2536, doi:10.1016/j.physd.2011.09.015.
  • Clamond, D., M. Francius, J. Grue, and C. Kharif (2006), Long time interaction of envelope solitons and freak wave formations, Eur. J. Mech. B Fluids, 25(5), 536553, doi:10.1016/j.euromechflu.2006.02.007.
  • Cooker, M. J., P. D. Weidman, and D. S. Bale (1997), Reflection of a high-amplitude solitary wave at a vertical wall, J. Fluid Mech., 342, 141158.
  • Craig, W., P. Guyenne, J. Hammack, D. Henderson, and C. Sulem (2006), Solitary water wave interactions, Phys. Fluids, 18(5), 57,106, doi:10.1063/1.2205916.
  • Dias, F., and P. Milewski (2010), On the fully-nonlinear shallow-water generalized Serre equations, Phys. Lett. A, 374(8), 10491053.
  • Dommermuth, D. (2000), The initialization of nonlinear waves using an adjustment scheme, Wave Motion, 32, 307317.
  • El, G. A., R. H. J. Grimshaw, and N. F. Smyth (2006), Unsteady undular bores in fully nonlinear shallow-water theory, Phys. Fluids, 18, 27,104.
  • Fenton, J. D., and M. M. Rienecker (1982), A Fourier method for solving nonlinear water-wave problems: Application to solitary-wave interactions, J. Fluid Mech., 118, 411443, doi:10.1017/S0022112082001141.
  • Goda, Y. (2010), Random Seas and Design of Maritime Structures, Adv. Ser. on Ocean Eng., vol. 33, World Sci., Singapore.
  • Green, A. E., and P. M. Naghdi (1976), A derivation of equations for wave propagation in water of variable depth, J. Fluid Mech., 78, 237246.
  • Green, A. E., N. Laws, and P. M. Naghdi (1974), On the theory of water waves, Proc. R. Soc. London, Ser. A, 338, 4355.
  • Hammack, J., D. Henderson, P. Guyenne, and M. Yi (2004), Solitary wave collisions, Proceedings of 23rd International Conference on Offshore Mechanics and Arctic Engineering, June 20-25, 2004, Vancouver, BC, Canada.
  • Hansom, J., and A. Hall (2009), Magnitude and frequency of extra-tropical North Atlantic cyclones: A chronology from cliff-top storm deposits, Quat. Int., 195, 4252.
  • Kelletat, D. (2008), Comments to Dawson, A. G. and Stewart, I. (2007). Tsunami deposits in the geological record.-Sedimentary Geology 200, 166-183, Sediment. Geol., 211, 8791.
  • Lannes, D., and P. Bonneton (2009), Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation, Phys. Fluids, 21, 016601.
  • Li, Y. A. (2002), Hamiltonian structure and linear stability of solitary waves of the Green-Naghdi equations, J. Nonlinear Math. Phys., 9(1), 99105.
  • Linton, C. M., and P. McIver (2001), Mathematical Techniques for Wave/Structure Interactions, 320 pp., Chapman and Hall, Loughborough University, UK.
  • Maxworthy, T. (1976), Experiments on collisions between solitary waves, J. Fluid. Mech., 76, 177185.
  • Mei, C. C. (1989), The Applied Dynamics of Ocean Surface Waves, World Sci., Singapore.
  • Mirchina, N. R., and E. Pelinovsky (1984), Increase in the amplitude of a long wave near a vertical wall, Izv. Atmos. Oceanic Phys., 20(3), 252253.
  • O'Brien, L., J. M. Dudley, and F. Dias (2013), Extreme wave events in Ireland: 14 680 BP–2012, Nat. Hazards and Earth Sys. Sci., 13(3), 625648, http://www.nat-hazards-earth-syst-sci.net/13/625/2013/, doi:10.5194/nhess-13-625-2013.
  • Pelinovsky, E. N., E. Troshina, V. Golinko, N. Osipenko, and N. Petrukhin (1999), Runup of tsunami waves on a vertical wall in a basin of complex topography, Phys. Chem. Earth B, 24(5), 431436.
  • Sainflou, M. (1928), Essai sur les digues maritimes verticales, Ann. Ponts Chaussées, 98(11), 548.
  • Scheffers, A., S. Scheffers, D. Kelletat, and T. Browne (2009), Wave-emplaced coarse debris and megaclasts in Ireland and Scotland: Boulder transport in a high-energy littoral environment, J. Geol., 117(5), 553573.
  • Scheffers, A., D. Kelletat, S. Haslett, S. Scheffers, and T. Browne (2010), Coastal boulder deposits in Galway Bay and the Aran Islands, western Ireland, Z. Geomorphol., 54(3), 247279.
  • Serre, F. (1953), Contribution à l'étude des écoulements permanents et variables dans les canaux, La Houille Blanche, 8, 374872.
  • Shampine, L. F. (1994), ODE solvers and the method of lines, Numer. Methods PDE, 10(6), 739755, doi:10.1002/num.1690100608.
  • Shampine, L. F., and M. W. Reichelt (1997), The MATLAB ODE Suite, SIAM J. Sci. Comput., 18, 122.
  • Stoker, J. J. (1957), Water Waves: The Mathematical Theory With Applications, Interscience, New York.
  • Su, C. H., and R. M. Mirie (1980), On head-on collisions between two solitary waves, J. Fluid Mech., 98, 509525.
  • Tissier, M., P. Bonneton, F. Marche, F. Chazel, and D. Lannes (2011), Nearshore dynamics of tsunami-like undular bores using a fully nonlinear Boussinesq model, J. Coastal Res., 64, 603607.
  • Wei, G., J. T. Kirby, S. T. Grilli, and R. Subramanya (1995), A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves, J. Fluid Mech., 294, 7192.
  • Williams, D. M. (2010), Mechanisms of wave transport of megaclasts on elevated cliff-top platforms: Examples from western Ireland relevant to the storm-wave versus tsunami controversy, Irish J. Earth Sci., 28, 1323.
  • Zabusky, N. J., and M. D. Kruskal (1965), Interaction of “solitons” in a collisionless plasma and the recurrence of initial states, Phys. Rev. Lett., 15, 240243.
  • Zheleznyak, M. I., and E. N. Pelinovsky (1985), Physical and mathematical models of the tsunami climbing a beach, in Tsunami Climbing a Beach, edited by Pelinovsky, E. N., Appl. Phys. Inst. Press, Gorky.