P. Boccotti, Wave Mechanics for Ocean Engineering, 2000.

W. Choi and R. Camassa, Exact Evolution Equations for Surface Waves, Journal of Engineering Mechanics, vol.125, issue.7, p.756, 1999.
DOI : 10.1061/(ASCE)0733-9399(1999)125:7(756)

D. G. Dommermuth and D. K. Yue, A high-order spectral method for the study of nonlinear gravity waves, Journal of Fluid Mechanics, vol.22, issue.-1, pp.267-288, 1987.
DOI : 10.1063/1.1694844

J. R. Dormand and P. J. Prince, A family of embedded Runge-Kutta formulae, Journal of Computational and Applied Mathematics, vol.6, issue.1, pp.19-26, 1980.
DOI : 10.1016/0771-050X(80)90013-3

A. I. Dyachenko, E. A. Kuznetsov, M. D. Spector, and V. E. Zakharov, Analytical description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping), Physics Letters A, vol.221, issue.1-2, pp.73-79, 1996.
DOI : 10.1016/0375-9601(96)00417-3

A. I. Dyachenko, V. E. Zakharov, and E. A. Kuznetsov, Nonlinear dynamics of the free surface of an ideal fluid, Plasma Physics Reports, vol.22, issue.10 3, pp.829-840, 1996.

K. B. Dysthe, K. Trulsen, H. E. Krogstad, and H. Socquet-juglard, Evolution of a narrow-band spectrum of random surface gravity waves, Journal of Fluid Mechanics, vol.478, issue.2, pp.1-10, 2003.
DOI : 10.1017/S0022112002002616

F. Fedele and F. Arena, Long-Term Statistics and Extreme Waves of Sea Storms, Journal of Physical Oceanography, vol.40, issue.5, pp.1106-1117, 2010.
DOI : 10.1175/2009JPO4335.1

F. Fedele and M. A. Tayfun, On nonlinear wave groups and crest statistics, Journal of Fluid Mechanics, vol.966, pp.221-239, 2003.
DOI : 10.1175/JPO2922.1

D. E. Hasselmann, M. Dunckel, and J. A. Ewing, Directional Wave Spectra Observed during JONSWAP 1973, Journal of Physical Oceanography, vol.10, issue.8, pp.1264-1280, 1980.
DOI : 10.1175/1520-0485(1980)010<1264:DWSODJ>2.0.CO;2

K. Hasselmann, On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory, Journal of Fluid Mechanics, vol.7, issue.04, pp.481-500, 1962.
DOI : 10.1017/S0022112062000373

K. Hasselmann, W. Sell, D. B. Ross, and P. Müller, A Parametric Wave Prediction Model, Journal of Physical Oceanography, vol.6, issue.2, pp.200-228, 1976.
DOI : 10.1175/1520-0485(1976)006<0200:APWPM>2.0.CO;2

K. Herterich and K. Hasselmann, A similarity relation for the nonlinear energy transfer in a finite-depth gravity-wave spectrum, Journal of Fluid Mechanics, vol.15, issue.01, pp.215-224, 1980.
DOI : 10.1175/1520-0485(1975)005 2.0.CO;2

S. J. Hogan, The Fourth-Order Evolution Equation for Deep-Water Gravity-Capillary Waves, Proc. R. Soc. A, pp.359-372, 1823.
DOI : 10.1098/rspa.1985.0122

P. A. Janssen, Nonlinear Four-Wave Interactions and Freak Waves, Journal of Physical Oceanography, vol.33, issue.4, pp.863-884, 2003.
DOI : 10.1175/1520-0485(2003)33<863:NFIAFW>2.0.CO;2

G. J. Komen, L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann et al., Dynamics and Modelling of Ocean Waves, 1996.
DOI : 10.1017/CBO9780511628955

B. Lapeyre and J. Lelong, A framework for adaptive Monte Carlo procedures, Monte Carlo Methods and Applications, vol.17, issue.1, pp.77-98, 2011.
DOI : 10.1515/mcma.2011.002

URL : https://hal.archives-ouvertes.fr/hal-00448864

Y. A. Li, J. M. Hyman, and W. Choi, A Numerical Study of the Exact Evolution Equations for Surface Waves in Water of Finite Depth, Studies in Applied Mathematics, vol.303, issue.3, pp.303-324, 2004.
DOI : 10.1111/j.0022-2526.2004.01534.x

P. Milewski, J. Vanden-broeck, and Z. Wang, Dynamics of steep two-dimensional gravity???capillary solitary waves, Journal of Fluid Mechanics, vol.200, issue.3, pp.466-477, 2010.
DOI : 10.1017/S0022112095001236

N. Mori and P. A. Janssen, On Kurtosis and Occurrence Probability of Freak Waves, Journal of Physical Oceanography, vol.36, issue.7, pp.1471-1483, 2005.
DOI : 10.1175/JPO2922.1

L. Shemer, A. Sergeeva, and D. Liberzon, Effect of the initial spectrum on the spatial evolution of statistics of unidirectional nonlinear random waves, Journal of Geophysical Research, vol.2, issue.C12, 2003.
DOI : 10.1029/2010JC006326

A. Slunyaev, C. Kharif, E. Pelinovsky, and T. Talipova, Nonlinear wave focusing on water of finite depth, Physica D: Nonlinear Phenomena, vol.173, issue.1-2, pp.77-96, 2002.
DOI : 10.1016/S0167-2789(02)00662-0

A. V. Slunyaev, A high-order nonlinear envelope equation for gravity waves in finite-depth water, Journal of Experimental and Theoretical Physics, vol.101, issue.5, pp.926-941, 2005.
DOI : 10.1134/1.2149072

H. Socquet-juglard, K. B. Dysthe, K. Trulsen, H. E. Krogstad, and J. Liu, Probability distributions of surface gravity waves during spectral changes, Journal of Fluid Mechanics, vol.542, issue.-1, pp.195-216, 2005.
DOI : 10.1017/S0022112005006312

J. J. Stoker, Water Waves, 1992.

A. Toffoli, M. Benoit, M. Onorato, and E. M. Bitner-gregersen, The effect of third-order nonlinearity on statistical properties of random directional waves in finite depth, Nonlinear Processes in Geophysics, vol.16, issue.1, pp.131-139, 2009.
DOI : 10.5194/npg-16-131-2009

C. Viotti, D. Dutykh, and F. Dias, The Conformal-mapping Method for Surface Gravity Waves in the Presence of Variable Bathymetry and Mean Current, Procedia IUTAM, vol.11, issue.3, pp.1-9, 2013.
DOI : 10.1016/j.piutam.2014.01.053

URL : https://hal.archives-ouvertes.fr/hal-00855780

C. Viotti, D. Dutykh, J. M. Dudley, and F. Dias, Emergence of coherent wave groups in deep-water random sea, Physical Review E, vol.87, issue.6, pp.63001-63004, 2013.
DOI : 10.1103/PhysRevE.87.063001

URL : https://hal.archives-ouvertes.fr/hal-00795397