M. Abramowitz, . Stegun, and . Ia, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1965.
DOI : 10.1119/1.1972842

Y. Agnon and C. Mei, Trapping and resonance of long shelf waves due to groups of short waves, Journal of Fluid Mechanics, vol.151, issue.-1, pp.201-221, 1988.
DOI : 10.1017/S0022112067001181

M. Antuono and M. Brocchini, The Boundary Value Problem for the Nonlinear Shallow Water Equations, Studies in Applied Mathematics, vol.445, issue.1, pp.73-93, 2007.
DOI : 10.1017/S002211208700329X

M. Antuono and M. Brocchini, Solving the nonlinear shallow-water equations in physical space, Journal of Fluid Mechanics, vol.119, pp.207-232, 2010.
DOI : 10.1017/S002211200700835X

M. Brocchini, . Peregrine, and . Dh, Integral flow properties of the swash zone and averaging, Journal of Fluid Mechanics, vol.129, issue.-1, pp.241-273, 1996.
DOI : 10.1016/0378-3839(89)90032-X

G. Carrier, Gravity waves on water of variable depth, Journal of Fluid Mechanics, vol.4, issue.04, pp.641-659, 1966.
DOI : 10.1017/S0022112066000892

G. Carrier, . Greenspan, and . Hp, Water waves of finite amplitude on a sloping beach, Journal of Fluid Mechanics, vol.1, issue.01, pp.97-109, 1958.
DOI : 10.1017/S0022112058000331

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

I. Didenkulova and E. Pelinovsky, Run-up of long waves on a beach: The influence of the incident wave form, Oceanology, vol.48, issue.1, pp.1-6, 2008.
DOI : 10.1134/S0001437008010013

D. Dutykh and F. Dias, Energy of tsunami waves generated by bottom motion, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.205, issue.5743, pp.725-744, 2009.
DOI : 10.1126/science.1114576
URL : https://hal.archives-ouvertes.fr/hal-00311752

D. Dutykh, . Katsaounis, and D. Mitsotakis, Finite volume schemes for dispersive wave propagation and runup, Journal of Computational Physics, vol.230, issue.8, pp.3035-3061, 2011.
DOI : 10.1016/j.jcp.2011.01.003
URL : https://hal.archives-ouvertes.fr/hal-00472431

D. Dutykh, . Poncet, and F. Dias, The VOLNA code for the numerical modeling of tsunami waves: Generation, propagation and inundation, European Journal of Mechanics - B/Fluids, vol.30, issue.6, pp.598-615, 2011.
DOI : 10.1016/j.euromechflu.2011.05.005

H. Fritz, W. Kongko, A. Moore, B. Mcadoo, J. Goff et al., Extreme runup from the 17 July 2006 Java tsunami, Geophysical Research Letters, vol.144, issue.3???4, p.12602, 2006.
DOI : 10.1029/2007GL029404

G. Grataloup and C. Mei, Localization of harmonics generated in nonlinear shallow water waves, Physical Review E, vol.68, issue.2, p.26314, 2003.
DOI : 10.1103/PhysRevE.68.026314

K. Kajiura, Local behaviour of tsunamis, Waves on Water of Variable Depth, pp.72-79, 1977.
DOI : 10.1007/3540082530_137

J. Keller and H. Keller, Water Wave Run-up on a Beach, ONR Research Report Contract No. NONR, issue.00, p.3828, 1964.

P. Madsen and H. Schaffer, Analytical solutions for tsunami runup on a plane beach: single waves, N-waves and transient waves, Journal of Fluid Mechanics, vol.39, issue.92, pp.27-57, 2010.
DOI : 10.1098/rspa.1994.0050

P. Madsen, . Fuhrman, and H. Schaffer, On the solitary wave paradigm for tsunamis, Journal of Geophysical Research, vol.402, issue.4, pp.12012-12034, 2008.
DOI : 10.1029/2008JC004932

W. Munk, . Snodgrass, and G. Freeman, Long waves on the continental shelf: an experiment to separate trapped and leaky modes, Journal of Fluid Mechanics, vol.43, issue.04, pp.529-554, 1964.
DOI : 10.1016/0146-6313(61)90018-1

S. Neetu, I. Suresh, R. Shankar, B. Nagarajan, R. Sharma et al., Trapped waves of the 27 November 1945 Makran tsunami: observations and numerical modeling, Natural Hazards, vol.116, issue.B1, pp.1609-1618, 2011.
DOI : 10.1007/s11069-011-9854-0

E. Pelinovsky, . Mazova, and . Rk, Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles, Natural Hazards, vol.74, issue.4, pp.227-249, 1992.
DOI : 10.1007/BF00129510

A. Rabinovich, . Leviant, and . As, Influence of Seiche Oscillations on the Formation of the Long-Wave Spectrum Near the Coast of the Southern Kuriles, Oceanology, vol.32, pp.17-23, 1992.

F. Serre, Contribution à l' Etude des Ecoulements Permanents et Variables Dans les Canaux, La Houille blanche, vol.8, pp.374-388, 1953.

T. Stefanakis, . Dias, and D. Dutykh, Local Run-Up Amplification by Resonant Wave Interactions, Physical Review Letters, vol.107, issue.12, p.124502, 2011.
DOI : 10.1103/PhysRevLett.107.124502
URL : http://arxiv.org/abs/1107.0304

C. Synolakis, The runup of solitary waves, Journal of Fluid Mechanics, vol.87, issue.-1, pp.523-545, 1987.
DOI : 10.1017/S0022112058000331

S. Tadepalli and C. Synolakis, The Run-Up of N-Waves on Sloping Beaches, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.445, issue.1923, pp.99-112, 1994.
DOI : 10.1098/rspa.1994.0050