J. Boussinesq, Essai sur la theorie des eaux courantes. Mémoires présentés par divers savants à l'Acad. des Sci. Inst, pp.1-680, 1877.

J. P. Boyd, Chebyshev and Fourier Spectral Methods, 2000.
DOI : 10.1007/978-3-642-83876-7

J. C. Bronski and M. A. Johnson, The Modulational Instability for a Generalized Kortewegde Vries Equation Archive for Rational Mechanics and Analysis, pp.357-400, 2010.

J. C. Bronski, M. A. Johnson, and T. Kapitula, An index theorem for the stability of periodic travelling waves of Korteweg???de Vries type, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.141, issue.06, pp.1411141-1173, 2011.
DOI : 10.1017/S0308210510001216

J. R. Cash and A. H. Karp, A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides, ACM Transactions on Mathematical Software, vol.16, issue.3, pp.201-222, 1990.
DOI : 10.1145/79505.79507

D. Dutykh and E. Tobisch, Direct dynamical energy cascade in the modified KdV equation, Physica D: Nonlinear Phenomena, vol.297, pp.1-33, 2014.
DOI : 10.1016/j.physd.2015.01.002

URL : https://hal.archives-ouvertes.fr/hal-00990724

D. Dutykh and E. Tobisch, Observation of the inverse energy cascade in the modified Korteweg-de Vries equation, EPL (Europhysics Letters), vol.107, issue.1, p.14001, 2014.
DOI : 10.1209/0295-5075/107/14001

URL : https://hal.archives-ouvertes.fr/hal-00991944

M. Frigo, A fast Fourier transform compiler, Proc. 1999 ACM SIGPLAN Conf. on Programming Language Design and Implementation, pp.169-180, 1999.

M. Frigo and S. G. Johnson, FFTW: an adaptive software architecture for the FFT, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181), pp.1381-1384, 1998.
DOI : 10.1109/ICASSP.1998.681704

M. Frigo and S. G. Johnson, The Design and Implementation of FFTW3, Proceedings of the IEEE, pp.216-231, 2005.
DOI : 10.1109/JPROC.2004.840301

R. Grimshaw, INTERNAL SOLITARY WAVES, Environmental Stratified Flows, pp.1-27, 2002.
DOI : 10.1142/9789812797568_0001

URL : https://hal.archives-ouvertes.fr/hal-00302108

R. Grimshaw, D. Pelinovsky, E. Pelinovsky, and T. Talipova, Wave group dynamics in weakly nonlinear long-wave models, Physica D: Nonlinear Phenomena, vol.159, issue.1-2, pp.35-57, 2001.
DOI : 10.1016/S0167-2789(01)00333-5

R. Grimshaw, E. Pelinovsky, T. Talipova, M. Ruderman, and R. Erdelyi, Short-Lived Large-Amplitude Pulses in the Nonlinear Long-Wave Model Described by the Modified Korteweg-De Vries Equation, Studies in Applied Mathematics, vol.147, issue.6, pp.189-210, 2005.
DOI : 10.1006/jdeq.1993.1040

E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential- Algebraic Problems, Series in Computational Mathematics, 1996.
DOI : 10.1007/978-3-642-05221-7

T. Y. Hou and R. Li, Computing nearly singular solutions using pseudo-spectral methods, Journal of Computational Physics, vol.226, issue.1, pp.379-397, 2007.
DOI : 10.1016/j.jcp.2007.04.014

URL : http://arxiv.org/abs/math/0701337

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

E. Kartashova, Energy spectra of 2D gravity and capillary waves with narrow frequency band excitation, EPL (Europhysics Letters), vol.97, issue.3, p.30004, 2012.
DOI : 10.1209/0295-5075/97/30004

E. Kartashova, Energy transport in weakly nonlinear wave systems with narrow frequency band excitation, Physical Review E, vol.86, issue.4, p.41129, 2012.
DOI : 10.1103/PhysRevE.86.041129

E. Kartashova, Time scales and structures of wave interaction exemplified with water waves, EPL (Europhysics Letters), vol.102, issue.4, p.44005, 2013.
DOI : 10.1209/0295-5075/102/44005

A. N. Kolmogorov, The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers, Proc. R. Soc. Lond. A, pp.9-13, 1890.
DOI : 10.1098/rspa.1991.0075

T. R. Marchant and N. F. Smyth, The extended Korteweg-de Vries equation and the resonant flow of a fluid over topography, Journal of Fluid Mechanics, vol.31, issue.-1, pp.263-287, 1990.
DOI : 10.1017/S0022112088001867

M. Onorato, A. R. Osborne, M. Serio, and S. Bertone, Freak Waves in Random Oceanic Sea States, Physical Review Letters, vol.86, issue.25, pp.5831-5834, 2001.
DOI : 10.1103/PhysRevLett.86.5831

L. F. Richardson, Weather prediction by numerical process, 1922.
DOI : 10.1017/CBO9780511618291

A. B. Shabat, E. Kartashova, and R. Linz, Computable Integrability. Chapter 1: General notions and ideas, 2005.

T. Tao, Scattering for the quartic generalised Korteweg???de Vries equation, Journal of Differential Equations, vol.232, issue.2, pp.623-651, 2007.
DOI : 10.1016/j.jde.2006.07.019

E. Tobisch, Energy spectrum of ensemble of weakly nonlinear gravity-capillary waves on a fluid surface, JETP, vol.119, issue.2, 2014.

L. N. Trefethen, Spectral methods in MatLab, Society for Industrial and Applied Mathematics, 2000.
DOI : 10.1137/1.9780898719598

V. E. Zakharov, V. S. Lvov, and G. Falkovich, Kolmogorov Spectra of Turbulence I. Wave Turbulence, Series in Nonlinear Dynamics, 1992.