C. J. Amick and J. F. Toland, The Semi-Analytic Theory of Standing Waves, Proc. Roy. Soc. Lond. A 411, pp.123-138, 1987.
DOI : 10.1098/rspa.1987.0057

D. Bambusi and S. Paleari, Families of Periodic Solutions of Resonant PDEs, Journal of Nonlinear Science, vol.11, issue.1, pp.69-87, 2001.
DOI : 10.1007/s003320010010

T. B. Benjamin and P. J. Olver, Hamiltonian structure, symmetries and conservation laws for water waves, Journal of Fluid Mechanics, vol.32, issue.-1, pp.137-187, 1982.
DOI : 10.1017/S0022112077001116

M. Berti and P. Bolle, Periodic Solutions of Nonlinear Wave Equations with General Nonlinearities, Communications in Mathematical Physics, vol.243, issue.2, pp.315-328, 2003.
DOI : 10.1007/s00220-003-0972-8

J. Boussinesq, Essai sur la théorie des eaux courantes, Mémoires présentés par divers savantsàsavantsà l'Académie des Sciences, pp.1-660, 1877.

H. Brezis, Periodic solutions of nonlinear vibrating strings and duality principles, Bulletin of the American Mathematical Society, vol.8, issue.3, pp.409-426, 1983.
DOI : 10.1090/S0273-0979-1983-15105-4

W. Craig and C. E. Wayne, Newton's method and periodic solutions of nonlinear wave equations, Communications on Pure and Applied Mathematics, vol.20, issue.11, pp.1409-1498, 1993.
DOI : 10.1002/cpa.3160461102

A. D. Craik, THE ORIGINS OF WATER WAVE THEORY, Annual Review of Fluid Mechanics, vol.36, issue.1, pp.1-28, 2004.
DOI : 10.1146/annurev.fluid.36.050802.122118

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

L. Hörmander, The boundary problems of physical geodesy, Arch. Rational Mech. Anal, vol.62, pp.1-52, 1976.

G. Iooss, The semi-analytic theory of standing waves, for several dominant modes, Proc. Roy. Soc. Lond. A455, pp.3513-3526, 1999.

G. Iooss, J. Plotnikov, and . Toland, Standing waves on infinite depth, Comptes Rendus Mathematique, vol.338, issue.5, pp.425-431, 2004.
DOI : 10.1016/j.crma.2004.01.002

URL : https://hal.archives-ouvertes.fr/hal-00014716

G. Iooss and J. F. Toland, Riemann-Hilbert and variational structure for standing waves
URL : https://hal.archives-ouvertes.fr/hal-00021613

T. Kato, Perturbation Theory for Linear Operators, 1966.

C. B. Morrey, Multiple Integrals in the Calculus of Variations, 1966.
DOI : 10.1007/978-3-540-69952-1

J. Moser, A rapidly convergent iteration method and non-linear partial differential equations I & II, Ann. Scuola Norm. Sup. Pisa, Sci. Fiz. Mat., III. Ser, vol.20, pp.265-315, 1966.

M. Okamura, Standing gravity waves of large amplitude in deep water, Wave Motion, vol.37, issue.2, pp.17-182, 2003.
DOI : 10.1016/S0165-2125(02)00055-0

G. W. Penney and A. T. Price, Part II. Finite Periodic Stationary Gravity Waves in a Perfect Liquid, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.244, issue.882, pp.254-284, 1952.
DOI : 10.1098/rsta.1952.0004

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

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.6337

S. D. Poisson, Mémoire sur la théorie des ondes (1816), Mém. Acad. R. Sci. Inst. France, 2nd Series, vol.1, pp.70-186, 1818.

P. S. Laplace, Suite des recherches sur plusieurs points du système du monde. (XXV-XXVII). Mém. présentés par divers savantsàsavantsà l, Acad. des Sciences

P. H. Rabinowitz, Free vibrations for a semilinear wave equation, Communications on Pure and Applied Mathematics, vol.13, issue.3, pp.31-68, 1978.
DOI : 10.1002/cpa.3160310103

L. Rayleigh, Deep Water Waves, Progressive or Stationary, to the Third Order of Approximation, Proc. R. Soc. London A 91, pp.345-353, 1915.
DOI : 10.1098/rspa.1915.0025

L. W. Schwartz and A. K. 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

G. G. Stokes, On the Theory of Oscillatory Waves, Trans. Camb. Phil. Soc, vol.8, pp.441-455, 1847.
DOI : 10.1017/CBO9780511702242.013

I. Tadjbaksh and J. B. Keller, Standing surface waves of finite amplitude, Journal of Fluid Mechanics, vol.244, issue.03, pp.442-451, 1960.
DOI : 10.1017/S0022112060000724

G. I. Taylor, An Experimental Study of Standing Waves, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.218, issue.1132, pp.44-59, 1953.
DOI : 10.1098/rspa.1953.0086

C. E. Wayne, Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory, Communications in Mathematical Physics, vol.21, issue.3, pp.479-528, 1990.
DOI : 10.1007/BF02104499

J. Wehausen, Free-surface flows, in Research Frontiers in Fluid Dynamics, 1965.

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

A. Zygmund, Trigonometric Series I & II, 1959.