The trajectories of particles in Stokes waves

Amick, C.J., Toland, J.F.: On periodic water-waves and their convergence to solitary waves in the long-wave limit. Philos. Trans. R. Soc. Lond., Ser. A 303, 633–669 (1981) Amick, C.J., Fraenkel, L.E., Toland, J.F.: On the Stokes conjecture for the wave of extreme form. Acta Math. 148, 193–214 (1982) Bryson, A.E.: Waves in Fluids. National Committee for Fluid Mechanics Films. Encyclopaedia Britannica Educational Corporation. 425 North Michigan Avenue, Chicago, IL 60611. Buffoni, B., Séré, É., Toland, J.F.: Minimization methods for quasi-linear problems with an application to periodic water waves. SIAM J. Math. Anal. 36, 1080–1094 (2005) Constantin, A.: On the deep water wave motion. J. Phys. A 34, 1405–1417 (2001) Constantin, A.: Edge waves along a sloping beach. J. Phys. A 34, 9723–9731 (2001) Constantin, A., Escher, J.: Symmetry of steady periodic surface water waves with vorticity. J. Fluid Mech. 498, 171–181 (2004) Constantin, A., Escher, J.: Symmetry of steady deep-water waves with vorticity. European J. Appl. Math. 15, 755–768 (2004) Constantin, A., Strauss, W.: Exact steady periodic water waves with vorticity. Comm. Pure Appl. Math. 57, 481–527 (2004) Constantin, A., Sattinger, D., Strauss, W.: Variational formulations for steady water waves with vorticity. J. Fluid. Mech. 548, 151–163 (2006) Constantin, A., Villari, G.: Particle trajectories in linear water waves. J. Math. Fluid. Mech., to appear. Craik, A.D.D.: The origins of water wave theory. Annu. Rev. Fluid Mech. 36, 1–28 (2004) Crapper, G.D.: Introduction to Water Waves. Chichester: Ellis Horwood Ltd. 1984 Debnath, L.: Nonlinear Water Waves. Boston, MA: Academic Press Inc. 1994 Fraenkel, L.E.: An Introduction to Maximum Principles and Symmetry in Elliptic Problems. Cambridge: Cambridge University Press 2000 Gerstner, F.: Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile. Ann. Phys. 2, 412–445 (1809) Johnson, R.S.: A Modern Introduction to the Mathematical Theory of Water Waves. Cambridge: Cambridge Univ. Press 1997 Keady, G., Norbury, J.: On the existence theory for irrotational water waves. Math. Proc. Camb. Philos. Soc. 83, 137–157 (1978) Lamb, H.: Hydrodynamics. Cambridge: Cambridge Univ. Press 1895 Levi-Civita, T.: Détermination rigoureuse des ondes permanentes d’ampleur finie. Math. Ann. 93, 264–314 (1925) Lewy, H.: A note on harmonic functions and a hydrodynamical application. Proc. Am. Math. Soc. 3, 111–113 (1952) Lighthill, J.: Waves in Fluids. Cambridge: Cambridge Univ. Press 1978 Longuet-Higgins, M.S.: The trajectories of particles in steep, symmetric gravity waves. J. Fluid Mech. 94, 497–517 (1979) Longuet-Higgins, M.S.: Eulerian and Lagrangian aspects of surface waves. J. Fluid Mech. 173, 683–707 (1986) Milne-Thomson, L.M.: Theoretical Hydrodynamics. London: The Macmillan Co. 1938 Okamoto, H., Sh-oji, M.: The Mathematical Theory of Permanent Progressive Water-waves. River Edge, NJ: World Scientific Publishing Co. Inc. 2001 Plotnikov, P.I., Toland, J.F.: Convexity of Stokes waves of extreme form. Arch. Ration. Mech. Anal. 171, 349–416 (2004) Rankine, W.J.M.: On the exact form of waves near the surface of deep water. Philos. Trans. R. Soc. Lond., Ser. A 153, 127–138 (1863) Sommerfeld, A.: Mechanics of Deformable Bodies. New York: Academic Press Inc. 1950 Spielvogel, E.R.: A variational principle for waves of infinite depth. Arch. Rational Mech. Anal. 39, 189–205 (1970) Stoker, J.J.: Water Waves. The Mathematical Theory with Applications. New York: Interscience Publ. Inc. 1957 Stokes, G.G.: On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441–455 (1847) Struik, D.J.: Détermination rigoureuse des ondes irrotationelles périodiques dans un canal à profondeur finie. Math. Ann. 95, 595–634 (1926) Toland, J.F.: Stokes waves. Topol. Methods Nonlinear Anal. 7, 1–48 (1996) Toland, J.F.: Stokes waves in Hardy spaces and as distributions. J. Math. Pures Appl. 79, 901–917 (2000) Yih, C.-S.: The role of drift mass in the kinetic energy and momentum of periodic water waves and sound waves. J. Fluid Mech. 331, 429–438 (1997)