T. Akylas, F. Dias, and R. Grimshaw, The effect of the induced mean flow on solitary waves in deep water, Journal of Fluid Mechanics, vol.355, pp.317-328, 1998.
DOI : 10.1017/S0022112097007714

C. Amick, Semilinear elliptic eigenvalue problems on an infinite strip with an application to stratified fluids, Ann. Scuola Norm. Sup. Pisa, vol.4, issue.11, pp.441-499, 1984.

C. Amick, On the theory of internal waves of permanent form in fluids of great depth, Transactions of the American Mathematical Society, vol.346, issue.2, pp.399-419, 1994.
DOI : 10.1090/S0002-9947-1994-1145726-1

C. Amick and K. Kirchgässner, A theory of solitary water-waves in the presence of surface tension, Archive for Rational Mechanics and Analysis, vol.105, issue.1, pp.1-49, 1989.
DOI : 10.1007/BF00251596

C. Amick and J. Toland, On solitary water-waves of finite amplitude, Archive for Rational Mechanics and Analysis, vol.76, issue.1, pp.9-95, 1981.
DOI : 10.1007/BF00250799

C. Amick and J. Toland, On Periodic Water-Waves and their Convergence to Solitary Waves in the Long-Wave Limit, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.303, issue.1481, pp.633-669, 1981.
DOI : 10.1098/rsta.1981.0231

C. Amick, L. Fraenkel, and J. Toland, On the stokes conjecture for the wave of extreme form, Acta Mathematica, vol.148, issue.0, pp.193-214, 1982.
DOI : 10.1007/BF02392728

C. Amick and J. Toland, The Semi-Analytic Theory of Standing Waves, Proc. Roy. Soc. Lond. A 411, pp.123-137, 1987.
DOI : 10.1098/rspa.1987.0057

C. Amick and R. E. Turner, A global theory of internal solitary waves in two-fluid systems, Transactions of the American Mathematical Society, vol.298, issue.2, pp.431-484, 1986.
DOI : 10.1090/S0002-9947-1986-0860375-3

C. Amick and R. E. Turner, Small internal waves in two-fluid systems, Archive for Rational Mechanics and Analysis, vol.13, issue.2, pp.111-139, 1989.
DOI : 10.1007/BF01053459

V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, 1983.

M. L. Banner and D. H. Peregrine, Wave Breaking in Deep Water, Annual Review of Fluid Mechanics, vol.25, issue.1, pp.373-397, 1993.
DOI : 10.1146/annurev.fl.25.010193.002105

M. Barrandon, R??sonance 1 : 2 pour les champs de vecteurs r??versibles, Comptes Rendus Mathematique, vol.334, issue.1, pp.7-10, 2002.
DOI : 10.1016/S1631-073X(02)02169-6

J. T. Beale, The existence of solitary water waves, Communications on Pure and Applied Mathematics, vol.28, issue.4, pp.373-389, 1977.
DOI : 10.1002/cpa.3160300402

J. T. Beale, Exact solitary water waves with capillary ripples at infinity, Communications on Pure and Applied Mathematics, vol.184, issue.2, pp.211-257, 1991.
DOI : 10.1002/cpa.3160440204

T. B. Benjamin, Internal waves of permanent form in fluids of great depth, Journal of Fluid Mechanics, vol.45, issue.03, pp.559-592, 1967.
DOI : 10.1017/S002211206700103X

J. Bona, D. K. Bose, and R. E. Turner, Finite amplitude steady waves in stratified fluid, J.Math. Pures et Appl, vol.62, pp.389-439, 1983.

J. Bona and J. C. Saut, See the paper in the next volume

T. Bridges, Hamiltonian spatial structure for three-dimensional water waves in a moving frame of reference, Journal of Nonlinear Science, vol.180, issue.5, pp.221-251, 1994.
DOI : 10.1007/BF02430633

T. Bridges and G. , Derks Dimension breaking of nonlinear elliptic PDEs: satisfying the spectral condition geometrically

T. Bridges and A. Mielke, A proof of the Benjamin-Feir instability, Archive for Rational Mechanics and Analysis, vol.9, issue.2, pp.145-198, 1995.
DOI : 10.1007/BF00376815

P. Bryant and M. Stiassnie, Different forms for nonlinear standing waves in deep water, Journal of Fluid Mechanics, vol.91, issue.-1, pp.135-156, 1994.
DOI : 10.1017/S0022112077001037

B. Buffoni, A. Champneys, and J. Toland, Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system, Journal of Dynamics and Differential Equations, vol.45, issue.2, pp.221-281, 1995.
DOI : 10.1007/BF02218892

B. Buffoni and M. D. Groves, A Multiplicity Result for Solitary Gravity-Capillary Waves in Deep Water via Critical-Point Theory, Archive for Rational Mechanics and Analysis, vol.146, issue.3, pp.183-220, 1999.
DOI : 10.1007/s002050050141

A. V. Buryak and A. R. Champneys, On the stability of solitary wave solutions of the fifth-order KdV equation, Physics Letters A, vol.233, issue.1-2, pp.58-62, 1997.
DOI : 10.1016/S0375-9601(97)00453-2

A. R. Champneys and J. Toland, Bifurcation of a plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems, Nonlinearity, vol.6, issue.5, pp.665-721, 1993.
DOI : 10.1088/0951-7715/6/5/002

A. R. Champneys, J. M. Vanden-broeck, and G. J. Lord, Do true elevation gravity???capillary solitary waves exist? A numerical investigation, Journal of Fluid Mechanics, vol.454, pp.403-417, 2002.
DOI : 10.1017/S0022112001007200

W. Craig, Birkhoff normal forms for water waves, Contemp. Math, vol.200, pp.57-74, 1996.
DOI : 10.1090/conm/200/02509

W. Craig and D. Nicholls, Traveling Two and Three Dimensional Capillary Gravity Water Waves, SIAM Journal on Mathematical Analysis, vol.32, issue.2, pp.323-359, 2000.
DOI : 10.1137/S0036141099354181

W. Craig and P. Wolfork, An integrable normal form for water waves in infinite depth, Physica D: Nonlinear Phenomena, vol.84, issue.3-4, pp.513-531, 1995.
DOI : 10.1016/0167-2789(95)00067-E

R. E. Davis and A. Acrivos, Solitary internal waves in deep water, Journal of Fluid Mechanics, vol.1, issue.03, pp.593-607, 1967.
DOI : 10.1017/S0022112067001041

F. Dias and M. , On the Transition from Two-Dimensional to Three-Dimensional Water Waves, Studies in Applied Mathematics, vol.104, issue.2, pp.91-127, 2000.
DOI : 10.1111/1467-9590.00132

F. Dias and A. , Interfacial waves with free-surface boundary conditions: an approach via a model equation, Physica D: Nonlinear Phenomena, vol.150, issue.3-4, pp.278-300, 2001.
DOI : 10.1016/S0167-2789(01)00149-X

F. Dias and G. Iooss, Capillary-gravity solitary waves with damped oscillations, Physica D: Nonlinear Phenomena, vol.65, issue.4, pp.399-423, 1993.
DOI : 10.1016/0167-2789(93)90064-8

F. Dias and G. Iooss, Capillary-gravity interfacial waves in infinite depth, Eur. J. Mech. B/Fluids, vol.15, issue.3, pp.367-393, 1996.

F. Dias and C. Kharif, NONLINEAR GRAVITY AND CAPILLARY-GRAVITY WAVES, Annual Review of Fluid Mechanics, vol.31, issue.1, pp.301-346, 1999.
DOI : 10.1146/annurev.fluid.31.1.301

F. Dias, D. Menasce, and J. M. Vanden-broeck, Numerical study of capillarygravity solitary waves, Eur. J. Mech. B/Fluids, vol.15, pp.17-36, 1996.

M. L. Dubreil-jacotin, ComplémentComplément`Complémentà une note antérieure sur les ondes de type permanent dans les liquides hétérogènes, Atti Accad. Lincei, Rend. Cl. Sci. Fis. Mat. Nat, vol.21, issue.6, pp.344-346, 1935.

A. I. Dyachenko and V. E. Zakharov, Is free surface hydrodynamics an integrable system? Phys. Letters A 190, pp.144-148, 1994.

D. M. Farmer and J. D. Smith, Tidal interaction of stratified flow with a sill in Knight Inlet. Deep-Sea Res, pp.239-254, 1980.

L. K. Forbes, Surface waves of large amplitude beneath an elastic sheet. Part 1. High-order series solution, Journal of Fluid Mechanics, vol.342, issue.-1, pp.409-428, 1986.
DOI : 10.1017/S0022112080002200

K. O. Friedrichs and D. H. Hyers, The existence of solitary waves, Communications on Pure and Applied Mathematics, vol.29, issue.3, pp.517-550, 1954.
DOI : 10.1002/cpa.3160070305

S. Grilli, P. Guyenne, and F. Dias, A fully non-linear model for three-dimensional overturning waves over an arbitrary bottom, International Journal for Numerical Methods in Fluids, vol.20, issue.7, pp.829-867, 2001.
DOI : 10.1002/1097-0363(20010415)35:7<829::AID-FLD115>3.0.CO;2-2

M. D. Groves, An existence theory for three-dimensional periodic travelling gravity???capillary water waves with bounded transverse profiles, Physica D: Nonlinear Phenomena, vol.152, issue.153, pp.395-415, 2001.
DOI : 10.1016/S0167-2789(01)00182-8

M. D. Groves, M. , and S. M. Sun, A dimension-breaking phenomenon in the theory of steady gravity-capillary water waves, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.360, issue.1799
DOI : 10.1098/rsta.2002.1066

M. D. Groves and A. Mielke, A spatial dynamics approach to three-dimensional gravity-capillary steady water waves, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.131, issue.01, pp.83-136, 2001.
DOI : 10.1017/S0308210500000809

M. D. Groves and J. F. Toland, On Variational Formulations??for Steady Water Waves, Archive for Rational Mechanics and Analysis, vol.137, issue.3, pp.203-226, 1997.
DOI : 10.1007/s002050050028

J. L. Hammack and D. M. Henderson, Resonant Interactions Among Surface Water Waves, Annual Review of Fluid Mechanics, vol.25, issue.1, pp.55-97, 1993.
DOI : 10.1146/annurev.fl.25.010193.000415

M. Courcelle and A. , Three-dimensional solitary waves in the presence of additional surface effects, European Journal of Mechanics - B/Fluids, vol.17, issue.5, pp.739-768, 1998.
DOI : 10.1016/S0997-7546(98)80023-X

M. and K. Kirchgässner, Breaking the dimension of a steady wave: some examples. Nonlinear dynamics and pattern formation in a natural environment, Notes Maths, vol.335, pp.119-129, 1995.

M. and K. Kirchgässner, Breaking the dimension of solitary waves Progress in partial differential equations: the Metz surveys 4. M.Chipot, I. Shafrir eds, Pitman Res. Notes in Maths, vol.345, pp.216-228, 1996.

M. Courcelle and K. Kirchgässner, Three-dimensional steady capillary -gravity waves. Ergodic Theory, Analysis, and Efficient Simulation of Dynamical systems, pp.363-397, 2001.

M. Courcelle and R. L. Pego, Travelling waves of the KP equations with transverse modulations, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.328, issue.3, pp.227-232, 1999.
DOI : 10.1016/S0764-4442(99)80126-8

A. Il-'ichev and K. Kirchgässner, Nonlinear water waves beneath an elastic icesheet, Sonderforschungsbereich, vol.19, issue.27, 1998.

G. Iooss, A codimension two bifurcation for reversible vector fields. Fields Institute Comm, pp.201-217, 1995.

G. Iooss, Existence d'orbites homoclines ?? un ??quilibre elliptique, pour un syst??me r??versible, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.324, issue.9, pp.993-997, 1997.
DOI : 10.1016/S0764-4442(97)87874-3

G. Iooss, Gravity and Capillary-Gravity Periodic Travelling Waves for Two Superposed Fluid Layers, One Being of Infinite Depth, Journal of Mathematical Fluid Mechanics, vol.1, issue.1, pp.24-61, 1999.
DOI : 10.1007/s000210050003

URL : https://hal.archives-ouvertes.fr/hal-01271096

G. Iooss, Semianalytic theory of standing waves in deep water, for several dominant modes, Proc. Roy. Soc. Lond. A, pp.3513-3526, 1999.

G. Iooss, On the Standing Wave Problem in Deep Water, Journal of Mathematical Fluid Mechanics, vol.4, issue.2
DOI : 10.1007/s00021-002-8541-z

URL : https://hal.archives-ouvertes.fr/hal-01271053

G. Iooss, Travelling waves in the Fermi-Pasta-Ulam lattice, Nonlinearity, vol.13, issue.3, pp.849-866, 2000.
DOI : 10.1088/0951-7715/13/3/319

URL : https://hal.archives-ouvertes.fr/hal-01271021

G. Iooss and M. Adelmeyer, Topics in Bifurcation Theory and Applications, Adv. Series in Nonlinear Dynamics World Sci. Pub, vol.3, 1998.

G. Iooss and K. Kirchgässner, Bifurcation d'ondes solitaires en présence d'une faible tension superficielle, C. R. Acad. Sci. Paris, vol.311, pp.265-268, 1990.

G. Iooss and K. Kirchgässner, Synopsis, Proc. Roy. Soc. Edinburgh 122A, pp.267-299, 1992.
DOI : 10.1090/S0273-0979-1982-15004-2

G. Iooss and P. Kirrmann, Capillary gravity waves on the free surface of an inviscid fluid of infinite depth. Existence of solitary waves, Archive for Rational Mechanics and Analysis, vol.240, issue.1, pp.1-19, 1996.
DOI : 10.1007/BF02199364

URL : https://hal.archives-ouvertes.fr/hal-01271137

G. Iooss, E. Lombardi, and S. M. Sun, Gravity travelling waves for two superposed fluid layers, one being of infinite depth: a new type of bifurcation, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.360, issue.1799, 2001.
DOI : 10.1098/rsta.2002.1071

URL : https://hal.archives-ouvertes.fr/hal-01271075

G. Iooss and J. Los, Bifurcation of spatially quasi-periodic solutions in hydrodynamic stability problems, Nonlinearity, vol.3, issue.3, pp.851-871, 1990.
DOI : 10.1088/0951-7715/3/3/014

G. Iooss and M. , Perturbed Homoclinic Solutions in Reversible 1:1 Resonance Vector Fields, Journal of Differential Equations, vol.102, issue.1, pp.62-88, 1993.
DOI : 10.1006/jdeq.1993.1022

URL : https://hal.archives-ouvertes.fr/hal-01271158

G. James, Internal Travelling Waves in the Limit of a Discontinuously Stratified Fluid, Archive for Rational Mechanics and Analysis, vol.160, issue.1, pp.41-90, 2001.
DOI : 10.1007/s002050100160

G. James, Small amplitude steady internal waves in stratified fluids, Ann. Univ. Ferrara, Sez VII, Sc. Mat, vol.XLIII, pp.65-119, 1997.

M. C. Jones, Group Invariances, Unfoldings and the Bifurcation of Capillary-Gravity Waves, International Journal of Bifurcation and Chaos, vol.07, issue.06, pp.1243-1266, 1997.
DOI : 10.1142/S021812749700100X

T. Kato, Perturbation theory for linear operators, 1966.

K. Kirchgässner, Wave-solutions of reversible systems and applications, Journal of Differential Equations, vol.45, issue.1, pp.113-127, 1982.
DOI : 10.1016/0022-0396(82)90058-4

K. Kirchgässner, Nonlinearly Resonant Surface Waves and Homoclinic Bifurcation, Adv. Appl. Mech, vol.26, pp.135-181, 1988.
DOI : 10.1016/S0065-2156(08)70288-6

K. Kirchgässner and K. Lankers, Structure of permanent waves in density-stratified media, Meccanica, vol.8, issue.4, pp.269-276, 1993.
DOI : 10.1007/BF00987162

P. Kirrmann, Reduktion nichtlinearer elliptischer Systeme in Zylindergebieten unter verwendung von optimaler Regularität in Hölder-Raümen, 1991.

Y. P. Krasovskii, On the theory of steady-state waves of finite amplitude, USSR Computational Mathematics and Mathematical Physics, vol.1, issue.4, pp.996-1018, 1961.
DOI : 10.1016/0041-5553(62)90025-3

K. Lankers and G. Friesecke, Fast, large-amplitude solitary waves in the 2D Euler equations for stratified fluids, Nonlinear Analysis: Theory, Methods & Applications, vol.29, issue.9, pp.1061-1078, 1997.
DOI : 10.1016/S0362-546X(96)00089-2

K. Lankers, Nichtlineare interne Wellen in dichtegesschichteten Flüssigkeiten, 1997.

M. A. Lavrentiev, A contribution to the theory of long waves (1943); On the theory of long waves Amer, Math. Soc. Translation, vol.102, pp.3-53, 1947.

T. Levi-civita, D???termination rigoureuse des ondes permanentes d'ampleur finie, Mathematische Annalen, vol.95, issue.1, pp.264-314, 1925.
DOI : 10.1007/BF01449965

E. Lombardi, Orbits Homoclinic to Exponentially Small Periodic Orbits for a Class of Reversible Systems. Application to Water Waves, Archive for Rational Mechanics and Analysis, vol.137, issue.3, pp.227-304, 1997.
DOI : 10.1007/s002050050029

E. Lombardi, Non-persistence of homoclinic connections for perturbed integrable reversible systems, Journal of Dynamics and Differential Equations, vol.11, issue.1, pp.129-208, 1999.
DOI : 10.1023/A:1021893602144

E. Lombardi, Oscillatory integrals and phenomena beyond all algebraic orders , with applications to homoclinic orbits in reversible systems, Lecture Notes in Maths, vol.1741, 2000.

E. Lombardi and G. Iooss, Gravity solitary waves with polynomial decay to exponentially small ripples at infinity. Preprint INLN, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01271079

M. S. Longuet-higgins and X. Zhang, Experiments on capillary-gravity waves of solitary type on deep water, Physics of Fluids, vol.9, issue.7, 1963.
DOI : 10.1063/1.869315

A. M. Lyapounov, Probì eme général de la stabilité du mouvement, Ann. Fac. Sci. Toulouse, vol.9, 1907.

R. S. Mackay and P. G. Saffman, Stability of Water Waves, Proc. Roy. Soc. London A 406, pp.115-125, 1986.
DOI : 10.1098/rspa.1986.0068

A. P. Metha and B. R. Sutherland, Interfacial gravity currents: Part II -wave excitation, Phys. Fluids

H. Michallet and E. Barthélemy, Experimental study of interfacial solitary waves, Journal of Fluid Mechanics, vol.366, pp.159-177, 1998.
DOI : 10.1017/S002211209800127X

H. Michallet and F. Dias, Numerical study of generalized interfacial solitary waves, Physics of Fluids, vol.11, issue.6, pp.1502-1511, 1999.
DOI : 10.1063/1.870013

A. Mielke, Reduction of quasilinear elliptic equations in cylindrical domains with applications, Mathematical Methods in the Applied Sciences, vol.55, issue.1, pp.51-66, 1988.
DOI : 10.1002/mma.1670100105

A. Mielke, Homoclinic and heteroclinic solutions in two-phase flow. Adv. Series in Nonlinear Dyn, Proc. IUTAM/ISIMM Symp. on Structure and Dynamics of Nonlinear waves in fluids, pp.353-362, 1995.

A. I. Nekrasov, On waves of permanent type. Izv. Ivanovo-Voznesensk, Politekhn . Inst, vol.3, pp.52-65, 1921.

H. Ono, Algebraic Solitary Waves in Stratified Fluids, Journal of the Physical Society of Japan, vol.39, issue.4, pp.1082-1091, 1975.
DOI : 10.1143/JPSJ.39.1082

E. Au and F. Dias, Interfacial periodic waves of permanent form with freesurface boundary conditions, J.Fluid Mech, vol.437, pp.325-336, 2001.

E. Au and F. Dias, Nonlinear effects in the response of a floating ice plate to a moving load, J. Fluid Mech

M. Perlin and W. W. Schultz, Capillary Effects on Surface Waves, Annual Review of Fluid Mechanics, vol.32, issue.1, pp.241-274, 2000.
DOI : 10.1146/annurev.fluid.32.1.241

P. I. Plotnikov and J. F. Toland, Nash-Moser Theory for Standing Water Waves, Archive for Rational Mechanics and Analysis, vol.159, issue.1, pp.1-83, 2001.
DOI : 10.1007/PL00004246

J. Reeder and M. Shinbrot, Three-dimensional, nonlinear wave interaction in water of constant depth, Nonlinear Analysis: Theory, Methods & Applications, vol.5, issue.3, pp.303-323, 1981.
DOI : 10.1016/0362-546X(81)90035-3

R. L. Sachs, On the existence of small amplitude solitary waves with strong surface tension, Journal of Differential Equations, vol.90, issue.1, pp.31-51, 1991.
DOI : 10.1016/0022-0396(91)90159-7

R. Scardovelli and S. Zaleski, DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW, Annual Review of Fluid Mechanics, vol.31, issue.1, pp.567-603, 1999.
DOI : 10.1146/annurev.fluid.31.1.567

G. Schneider and C. E. Wayne, The long-wave limit for the water wave problem I. The case of zero surface tension, Communications on Pure and Applied Mathematics, vol.15, issue.12, pp.1475-1535, 2000.
DOI : 10.1002/1097-0312(200012)53:12<1475::AID-CPA1>3.0.CO;2-V

L. Schwartz and A. Whitney, A semi-analytic solution for nonlinear standing waves in deep water, Journal of Fluid Mechanics, vol.91, issue.-1, pp.147-171, 1981.
DOI : 10.1017/S0022112062000622

V. A. Squire, R. J. Hosking, A. D. Kerr, and P. J. Langhorne, Moving loads on ice plates. Solids Mechanics and its Applications, 1996.

V. A. Squire, W. H. Robinson, P. J. Langhorne, and T. G. Haskell, Vehicles and aircraft on floating ice, Nature, vol.333, issue.6169, pp.159-161, 1988.
DOI : 10.1038/333159a0

G. G. Stokes, On the theory of oscillatory waves. Camb, Phil. Soc. Trans, vol.8, pp.441-455, 1847.

S. M. Sun, Existence of a generalized solitary wave solution for water with positive bond number less than 13, Journal of Mathematical Analysis and Applications, vol.156, issue.2, pp.471-504, 1991.
DOI : 10.1016/0022-247X(91)90410-2

S. M. Sun, Non-existence of truly solitary waves in water with small surface tension, Proc. Roy. Soc. London A 455, pp.2191-2228, 1999.
DOI : 10.1098/rspa.1999.0399

S. M. Sun, Some analytical properties of capillary-gravity waves in two-fluid flows of infinite depth, Proc. Roy. Soc. London A 453, pp.1153-1175, 1997.
DOI : 10.1098/rspa.1997.0064

S. M. Sun, Existence of solitary internal waves in a two-layer fluid of infinite depth, Nonlinear Analysis: Theory, Methods & Applications, vol.30, issue.8, pp.5481-5490, 1997.
DOI : 10.1016/S0362-546X(97)00178-8

S. M. Sun and M. C. Shen, Exponentially Small Estimate for the Amplitude of Capillary Ripples of a Generalized Solitary Wave, Journal of Mathematical Analysis and Applications, vol.172, issue.2, pp.533-566, 1993.
DOI : 10.1006/jmaa.1993.1042

S. M. Sun and M. C. Shen, Exact Theory of Generalized Solitary Waves in a Two-Layer Liquid in the Absence of Surface Tension, Journal of Mathematical Analysis and Applications, vol.180, issue.1, pp.245-274, 1993.
DOI : 10.1006/jmaa.1993.1400

T. Takizawa, Field studies on response of a floating sea ice sheet to a steadily moving load. Contributions from the Institute of Low temperature Science A 36, pp.31-76, 1987.

J. F. Toland, Stokes waves. Topological Meth, Nonlinear Anal. 7 and, pp.1-48, 1996.

W. Tsai and D. K. Yue, Computation of Nonlinear Free-Surface Flows, Annual Review of Fluid Mechanics, vol.28, issue.1, pp.249-278, 1996.
DOI : 10.1146/annurev.fl.28.010196.001341

R. E. Turner, Internal waves in fluids with rapidly varying density, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.8, pp.513-573, 1981.

A. Vanderbauwhede and G. Iooss, Center manifold theory in infinite dimensions . Dynamics Reported, 1 New series, pp.125-163, 1992.

J. V. Wehausen and E. V. Laitone, Surface waves. Handbuch der Physik, Ed. S. Flügge, vol.9, pp.446-778, 1960.

P. D. Woods and A. R. Champneys, Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian???Hopf bifurcation, Physica D: Nonlinear Phenomena, vol.129, issue.3-4, pp.147-170, 1999.
DOI : 10.1016/S0167-2789(98)00309-1

S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Inventiones Mathematicae, vol.130, issue.1, pp.39-72, 1997.
DOI : 10.1007/s002220050177

S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Inventiones Mathematicae, vol.130, issue.1, pp.445-495, 1999.
DOI : 10.1007/s002220050177

T. S. Yang and T. R. Akylas, Weakly nonlocal gravity???capillary solitary waves, Physics of Fluids, vol.8, issue.6, pp.1506-1514, 1996.
DOI : 10.1063/1.868926

T. S. Yang and T. R. Akylas, On asymmetric gravity???capillary solitary waves, Journal of Fluid Mechanics, vol.330, pp.215-232, 1997.
DOI : 10.1017/S0022112096003643

X. Zhang, Capillary???gravity and capillary waves generated in a wind wave tank: observations and theories, Journal of Fluid Mechanics, vol.95, issue.-1, pp.51-82, 1995.
DOI : 10.1016/0169-5983(88)90005-6

V. E. Zakharov, Stability of periodic waves of finite amplitude on the surface of a deep fluid, Journal of Applied Mechanics and Technical Physics, vol.10, issue.no. 4, pp.190-194, 1968.
DOI : 10.1007/BF00913182