M. Benoit, ContributionàContributionà l'´ etude desétatsdesétats de mer et des vagues, depuis l'océan jusqu'aux ouvrages cotiers, p.12, 2006.

J. L. Bona, W. G. Pritchard, and L. R. Scott, An Evaluation of a Model Equation for Water Waves, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.302, issue.1471, pp.457-510, 1981.
DOI : 10.1098/rsta.1981.0178

J. L. Bona, M. Chen, and J. Saut, Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory, Journal of Nonlinear Science, vol.12, issue.4, pp.283-318, 2002.
DOI : 10.1007/s00332-002-0466-4

J. Boussinesq, Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond, J. Math. Pures Appl, vol.17, issue.2, pp.55-108

J. Boussinesq, Essai sur la théorie des eaux courantes. Mémoires présentés par divers SavantsàSavantsà l, Académie des Sciences, vol.23, issue.5, pp.1-680

J. Boussinesq, Lois de l'extinction de la houle en haute mer, C. R. Acad. Sc. Paris, vol.121, issue.4, pp.15-20, 1895.

J. V. Boussinesq, Théorie générale des mouvements qui sont propagés dans un canal rectangulaire horizontal, C. R. Acad. Sc. Paris, vol.73, issue.2, pp.256-260

M. Chen, Exact traveling-wave solutions to bidirectional wave equations, International Journal of Theoretical Physics, vol.37, issue.5, pp.1547-1567, 1998.
DOI : 10.1023/A:1026667903256

A. J. De-saint-venant, Théorie du mouvement non-permanent des eaux, avec application aux crues desrivì eres etàetà l'introduction des marées dans leur lit, C. R. Acad. Sc. Paris, vol.73, issue.2, pp.147-154

F. Dias, A. I. Dyachenko, and V. E. Zakharov, Theory of weakly damped free-surface flows: A new formulation based on potential flow solutions, Physics Letters A, vol.372, issue.8, 2007.
DOI : 10.1016/j.physleta.2007.09.027

D. Dutykh and F. Dias, Viscous potential free-surface flows in a fluid layer of finite depth, Comptes Rendus Mathematique, vol.345, issue.2, pp.113-118, 2007.
DOI : 10.1016/j.crma.2007.06.007

URL : https://hal.archives-ouvertes.fr/hal-00145315

D. Dutykh and F. Dias, Water waves generated by a moving bottom, Tsunami and Nonlinear waves, pp.63-94, 2007.
DOI : 10.1007/978-3-540-71256-5_4

URL : https://hal.archives-ouvertes.fr/hal-00115875

K. L. Heitner and G. W. Housner, Numerical model for tsunami runup, J. Waterway, Port, Coastal and Ocean Engineering, vol.96, issue.5, pp.701-719, 1970.

L. Jiang, C. Ting, M. Perlin, and W. W. Schultz, Moderate and steep Faraday waves: instabilities, modulation and temporal asymmetries, Journal of Fluid Mechanics, vol.13, issue.-1, pp.275-307, 1996.
DOI : 10.1016/0309-1708(81)90027-0

A. B. Kennedy, Q. Chen, J. T. Kirby, and R. A. Dalrymple, Boussinesq Modeling of Wave Transformation, Breaking, and Runup.???I: 1D, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol.126, issue.1, pp.39-47, 2000.
DOI : 10.1061/(ASCE)0733-950X(2000)126:1(39)

J. T. Kirby, Advances in Coastal Modeling chapter Boussinesq models and applications to nearshore wave propagation, surfzone processes and wave-induced currents, pp.1-41, 2003.

H. Lamb, Hydrodynamics, 6th edn, 1932.

M. S. Longuet-higgins, Theory of weakly damped Stokes waves: a new formulation and its physical interpretation, Journal of Fluid Mechanics, vol.245, issue.-1, pp.319-324, 1992.
DOI : 10.1017/S002211206000061X

P. A. Madsen and H. A. Schaffer, Higher-order Boussinesq-type equations for surface gravity waves: derivation and analysis, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.356, issue.1749, pp.3123-3184, 1998.
DOI : 10.1098/rsta.1998.0309

P. A. Madsen, R. Murray, and O. R. Sorensen, A new form of the Boussinesq equations with improved linear dispersion characteristics, Coastal Engineering, vol.15, issue.4, pp.371-388, 1991.
DOI : 10.1016/0378-3839(91)90017-B

J. Murray, Short wave modelling using new equations of boussinesq type, Proc., 9th Australian Conf. on Coast. and Oc. Engrg, p.25, 1989.

A. C. Newell, Finite Amplitude Instabilities of Partial Difference Equations, SIAM Journal on Applied Mathematics, vol.33, issue.1, pp.133-160, 1977.
DOI : 10.1137/0133010

O. Nwogu, Alternative Form of Boussinesq Equations for Nearshore Wave Propagation, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol.119, issue.6, pp.618-638, 1993.
DOI : 10.1061/(ASCE)0733-950X(1993)119:6(618)

D. H. Peregrine, Long waves on a beach, Journal of Fluid Mechanics, vol.13, issue.04, pp.815-827, 1967.
DOI : 10.1017/S0022112067002605

D. H. Peregrine, Waves on Beaches and Resulting Sediment Transport, chapter Equations for water waves and the approximation behind them, pp.95-121, 1972.

K. D. Ruvinsky, F. I. Feldstein, and G. I. Freidman, Numerical simulations of the quasi-stationary stage of ripple excitation by steep gravity???capillary waves, Journal of Fluid Mechanics, vol.2, issue.-1, pp.339-353, 1991.
DOI : 10.1017/S0022112079001373

C. Skandrani, J. Kharif, and . Poitevin, Nonlinear evolution of water surface waves: the frequency down-shift phenomenon, Contemp. Math, vol.200, issue.5, pp.157-171, 1996.
DOI : 10.1090/conm/200/02514

B. Spivak, J. Vanden-broeck, and T. Miloh, Free-surface wave damping due to viscosity and surfactants, European Journal of Mechanics - B/Fluids, vol.21, issue.2, pp.207-224, 2002.
DOI : 10.1016/S0997-7546(01)01178-5

E. O. Tuck, The effect of a surface layer of viscous fluid on the wave resistance of a thin ship, J. Ship Research, vol.18, issue.5, pp.265-271, 1974.

J. T. Wei, S. T. Kirby, R. Grilli, and . 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

G. B. Whitham, Linear and nonlinear waves, p.20, 1999.
DOI : 10.1002/9781118032954

J. M. Witting, A unified model for the evolution nonlinear water waves, Journal of Computational Physics, vol.56, issue.2, pp.203-236, 1984.
DOI : 10.1016/0021-9991(84)90092-5

J. A. Zelt, The run-up of nonbreaking and breaking solitary waves, Coastal Engineering, vol.15, issue.3, pp.205-246, 1991.
DOI : 10.1016/0378-3839(91)90003-Y

W. Zhang and J. Vinals, Pattern formation in weakly damped parametric surface waves, Journal of Fluid Mechanics, vol.336, issue.8, pp.301-330, 1997.
DOI : 10.1017/S0022112096004764