Alazard T., Burq N., Zuily C.: On the water-wave equations with surface tension. Duke Math. J., 158(3), 413–499 (2011)
Alazard, T., Delort, J.-M.: Sobolev estimates for two dimensional gravity water waves. Preprint, (2013)
Alazard T., Métivier G.: Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Commun. Partial Differ. Equ. 34(10-12), 1632–1704 (2009)
Alinhac S.: Paracomposition et opérateurs paradifférentiels. Commun. Partial Differ. Equ. 11(1), 87–121 (1986)
Alinhac S.: Existence d’ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels. Commun Partial Differ. Equ. 14(2), 173–230 (1989)
Baldi P.: Periodic solutions of forced Kirchhoff equations. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 8(1), 117–141 (2009)
Baldi P.: Periodic solutions of fully nonlinear autonomous equations of Benjamin-Ono type. Ann. Inst. H. Poincaré Anal. Non Linéaire 30(1), 33–77 (2013)
Baldi P., Berti M., Montalto R.: KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation. Math. Ann. 359(1-2), 471–536 (2014)
Baldi, P., Berti, M., Montalto, R.: KAM for autonomous quasi-linear perturbations of KdV. Preprint (2014) arXiv:1404.3125
Barber, N.: Water Waves. Wykeham Publications, (1969)
Berti M., Biasco L., Procesi M.: KAM theory for the Hamiltonian derivative wave equation. Ann. Sci. Éc. Norm. Supér. (4), 46(2), 301–373 (2013)
Berti M., Biasco L., Procesi M.: KAM for Reversible Derivative Wave Equations. Arch. Ration. Mech. Anal. 212(3), 905–955 (2014)
Beyer K., Günther M.: On the Cauchy problem for a capillary drop. I. Irrotational motion. Math. Methods Appl. Sci. 21(12), 1149–1183 (1998)
Bony J.-M.: Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. École Norm. Sup. (4) 14(2), 209–246 (1981)
Bourgain, J.: Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. Internat. Math. Res. Notices, (11):475ff., approx. 21 pp. (electronic), (1994)
Bourgain, J.: Periodic Solutions of Nonlinear Wave Equations. In: Harmonic analysis and partial differential equations (Chicago, IL, 1996), Chicago Lectures in Math., pp. 69–97. Univ. Chicago Press, Chicago, IL, (1999)
Bridges T.J., Dias F., Menasce D.: Steady three-dimensional water-wave patterns on a finite-depth fluid. J. Fluid Mech. 436, 145–175 (2001)
Buffoni B., Groves M.D., Sun S.-M., Wahlén E.: Existence and conditional energetic stability of three-dimensional fully localized solitary gravity-capillary water waves. J. Differ. Equ. 254(3), 1006–1096 (2013)
Craig, W.: Problèmes de petits diviseurs dans les équations aux dérivées partielles. In: Panoramas et Synthèses [Panoramas and Syntheses], vol. 9. Société Mathématique de France, Paris (2000)
Craig W., Nicholls D.P.: Travelling two and three dimensional capillary gravity water waves. SIAM J. Math. Anal. 32(2), 323–359 (2000) (electronic)
Craig W., Nicholls D.P.: Traveling gravity water waves in two and three dimensions. Eur. J. Mech. B Fluids 21(6), 615–641 (2002)
Craig W., Schanz U., Sulem C.: The modulational regime of three-dimensional water waves and the Davey-Stewartson system. Ann. Inst. H. Poincaré Anal. Non Linéaire 14(5), 615–667 (1997)
Craig W., Sulem C.: Numerical simulation of gravity waves. J. Comput. Phys. 108(1), 73–83 (1993)
Dias F., Kharif C.: Nonlinear gravity and capillary-gravity waves. Ann. Rev. Fluid Mech. 31(1), 301–346 (1999)
Groves M.D.: Steady water waves. J. Nonlinear Math. Phys. 11(4), 435–460 (2004)
Groves M.D., Haragus M.: A bifurcation theory for three-dimensional oblique travelling gravity-capillary water waves. J. Nonlinear Sci. 13(4), 397–447 (2003)
Hörmander, L.: The analysis of linear partial differential operators I. Distribution theory and Fourier analysis. Springer-Verlag, Berlin (1990)
Iooss, G.: Small divisor problems in fluid mechanics. J. Dyn. Diff. Equ. (2013). doi:10.1007/s10884-013-9317-2
Iooss G., Plotnikov P.I.: Existence of multimodal standing gravity waves. J. Math. Fluid Mech. 7(suppl. 3), S349–S364 (2005)
Iooss G., Plotnikov P.I.: Multimodal standing gravity waves: a completely resonant system. J. Math. Fluid Mech. 7(suppl. 1), S110–S126 (2005)
Iooss, G., Plotnikov, P.I.: Small divisor problem in the theory of three-dimensional water gravity waves. Mem. Amer. Math. Soc. 200(940), viii+128 (2009)
Iooss G., Plotnikov P.I.: Asymmetrical tridimensional travelling gravity waves. Arch. Rat. Mech. Anal. 200(3), 789–880 (2011)
Iooss G., Plotnikov P.I., Toland J.F.: Standing waves on an infinitely deep perfect fluid under gravity. Arch. Ration. Mech. Anal. 177(3), 367–478 (2005)
Kappeler, T., Pöschel, J.: KdV & KAM. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas, vol. 45, 3rd Series. A Series of Modern Surveys in Mathematics]. Springer-Verlag, Berlin (2003)
Klainerman S., Majda A.: Formation of singularities for wave equations including the nonlinear vibrating string. Commun. Pure Appl. Math. 33(3), 241–263 (1980)
Kuksin, S.B.: Hamiltonian perturbations of infinite-dimensional linear systems with imaginary spectrum. Funkt. Anal. i Prilozhen 21(3), 22–37, 95, (1987)
Kuksin, S.B.: Analysis of Hamiltonian PDEs. Oxford Lecture Series in Mathematics and its Applications, vol. 19. Oxford University Press, Oxford (2000)
Lannes D.: Well-posedness of the water-waves equations. J. Am. Math. Soc. 18(3), 605–654 (2005) (electronic)
Lannes, D.: The water waves problem: mathematical analysis and asymptotics. Math. Surv. Monogr. 188 (2013)
Liu J., Yuan X.: A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations. Commun. Math. Phys. 307(3), 629–673 (2011)
Ming, M., Rousset, F., Tzvetkov, N.: Multi-solitons and related solutions for the water-waves system. arXiv:1304.5263
Ming M., Zhang Z.: Well-posedness of the water-wave problem with surface tension. J. Math. Pures Appl. (9) 92(5), 429–455 (2009)
Plotnikov P.I., Toland J.F.: Nash-Moser theory for standing water waves. Arch. Ration. Mech. Anal. 159(1), 1–83 (2001)
Rabinowitz P.H.: Periodic solutions of nonlinear hyperbolic partial differential equations. Commun. Pure Appl. Math. 20, 145–205 (1967)
Rabinowitz P.H.: Periodic solutions of nonlinear hyperbolic partial differential equations. II. Commun. Pure Appl. Math. 22, 15–39 (1968)
Reeder J., Shinbrot M.: Three-dimensional, nonlinear wave interaction in water of constant depth. Nonlinear Anal. 5(3), 303–323 (1981)
Sulem, C., Sulem, P.-L.: The nonlinear Schrödinger equation. Applied Mathematical Sciences, vol. 139. Springer-Verlag, New York (1999) (Self-focusing and wave collapse)
Wayne C.: Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory. Commun. Math. Phys. 127(3), 479–528 (1990)
Zakharov V.E.: Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9(2), 190–194 (1968)
Zhang J., Gao M., Yuan X.: KAM tori for reversible partial differential equations. Nonlinearity 24(4), 1189–1228 (2011)