On the Fluid Motion in Standing Waves

References

• Amick , C J and Toland , J F . 1981 . On Periodic water-waves and their convergence to solitary waves in the long-wave limit . Philos. Trans. Roy. Soc. London Ser. A , 303 : 633 – 669 .
   Google Scholar
• Buffoni , B , Séré , E and Toland , J F . 2005 . Minimization methods for quasi-linear problems with an application to periodic water waves . SIAM J. Math. Anal. , 36 : 1080 – 1094 .
   Google Scholar
• Constantin , A . 2001 . Edge Waves Along A Sloping beach . J. Phys. A , 34 : 9723 – 9731 .
   Google Scholar
• Constantin , A . 2001 . On The Deep Water Wave Motion . J. Phys. A , 34 : 1405 – 1417 .
   Google Scholar
• Constantin , A . 2006 . The Trajectories Of Particles in Stokes waves . Invent. Math. , 166 : 523 – 535 .
   Web of Science ®Google Scholar
• Constantin , A , Ehrnström , M and Villari , G . 2008 . Particle trajectories in linear deep-water waves . Nonlinear Anal. Real World Appl. , 9 : 1336 – 1344 .
   Web of Science ®Google Scholar
• Constantin , A and Escher , J . 2007 . Particle Trajectories in solitary water waves . Bull. Amer. Math. Soc. , 44 : 423 – 431 .
   Web of Science ®Google Scholar
• Constantin , A , Sattinger , D and Strauss , W . 2006 . Variational formulations for steady water waves with vorticity . J. Livid Mech. , 548 : 151 – 163 .
   Google Scholar
• Constantin , A and Strauss , W . 2004 . Exact Steady periodic water waves with vorticity . Comm. Pvre Appl. Math. , 57 : 481 – 527 .
   Web of Science ®Google Scholar
• Constantin , A and Strauss , W . 2007 . Stability properties of steady water waves with vorticity . Comm. Pvre Appl. Math. , 60 : 911 – 950 .
   Web of Science ®Google Scholar
• Constantin , A and Villari , G . 2008 . Particle Trajectories in linear water waves . J. Math. Fluid Mech , 10 : 1 – 18 .
   Web of Science ®Google Scholar
• Add , Craik . 2004 . “ The Origins Of Water Wave Theory, in: Annual review of fluid mechanics ” . In Annv. Rev. Fluid Mech , Vol. 36 of , 1 – 28 . Palo Alto , , CA : Annual Reviews . Vol. 36, Vol
   Google Scholar
• Dean , R G and Dalrymple , R A . 1991 . Water Wave mechanics for engineers and scientists , Singapore : World Scientific .
   Google Scholar
• Ehrnström , M . 2008 . On The Streamlines And Particle paths of gravitational water waves . Nonlinearity , 21 : 1 – 14 .
   Google Scholar
• Ehrnström , M and Villari , G . 2008 . Linear Water waves with vorticity: rotational features and particle paths . J. Differential Eqvations , 244 : 1888 – 1909 .
   Google Scholar
• Gerstner , F . 1809 . Theorie Der Wellen Samt Einer daraus abgeleiteten Theorie der Deichprofile . Ann. Phys. , 2 : 412 – 445 .
   Google Scholar
• Groves , M D . 2004 . Steady Water Waves . J. Nonlinear Math. Phys. , 11 : 435 – 460 .
   Web of Science ®Google Scholar
• Henry , D . 2006 . The Trajectories Of Particles in deep-water Stokes waves . International Mathematics Research Notices , 2006 : 1 – 13 .
   Google Scholar
• Henry , D . 2007 . Particle Trajectories In Linear periodic capillary and capillary-gravity deep-water waves . J. Nonlinear Math. Phys. , 14 : 1 – 7 .
   Web of Science ®Google Scholar
• Iooss , G and Plotnikov , P . 2005 . Existence Of multimodal standing gravity waves . J. Math. Fluid Mech. , 7 : S349 – S364 .
   Google Scholar
• Iooss , G , Plotnikov , P I and Toland , J F . 2004 . Standing waves on infinite depth . C. R. Math. Acad. Sci. Paris , 338 : 425 – 431 .
   Google Scholar
• Iooss , G , Plotnikov , P I and Toland , J F . 2005 . Standing waves on an infinitely deep perfect fluid under gravity . Arch. Ration. Mech. Anal. , 177 : 367 – 478 .
   Google Scholar
• Johnson , R S . 1997 . “ A Modern Introduction to the mathematical theory of water waves ” . In Cambridge Texts in Applied Mathematics , Cambridge : Cambridge University Press .
   Google Scholar
• Lawden , D F . 1989 . Elliptic Functions And applications, Vol. 80 of Applied Mathematical Sciences , New York : Springer-Verlag .
   Google Scholar
• Lighthill , J . 1978 . Waves In Fluids , Cambridge : Cambridge University Press .
   Google Scholar
• Okamoto , H and Shoji , M . 2001 . The Mathematical theory of permanent progressive water-waves, Vol. 20 of Advanced Series in Nonlinear Dynamics , River Edge , , NJ : World Scientific Publishing Co. Inc .
   Google Scholar
• Penney , G W and Price , A T . 1952 . Finite periodic stationary gravity waves in a perfect fluid . Phil. Trans. Roy. Soc. A , 244 : 254 – 284 .
   Web of Science ®Google Scholar
• Plotnikov , P I and Toland , J F . 2001 . Nash-Moser theory for standing water waves . Arch. Ration. Mech. Anal. , 159 : 1 – 83 .
   Google Scholar
• Rankine , W J M . 1863 . On The Exact Form of waves near the surface of deep water . Phil. Trans. Roy. Soc. London Ser. A , 153 : 127 – 138 .
   Google Scholar
• Ruellan , F and Wallet , A . 1950 . Trajectoires internes dans un clapotis partiel . La Hoville Blanche , 5 : 483 – 489 .
   Google Scholar
• Wahlén , E . 2006 . Steady Periodic Capillary-gravity waves with vorticity . SIAM J. Math. Anal. , 38 : 921 – 943 .
   Google Scholar