Gravity solitary waves with polynomial decay to exponentially small ripples at infinity

E. Lombardi; G. Iooss

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 4, page 669-704
  • ISSN: 0294-1449

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Lombardi, E., and Iooss, G.. "Gravity solitary waves with polynomial decay to exponentially small ripples at infinity." Annales de l'I.H.P. Analyse non linéaire 20.4 (2003): 669-704. <http://eudml.org/doc/78593>.

@article{Lombardi2003,
author = {Lombardi, E., Iooss, G.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {existence; analytic continuation; exponentially small upper bounds; oscillatory integrals},
language = {eng},
number = {4},
pages = {669-704},
publisher = {Elsevier},
title = {Gravity solitary waves with polynomial decay to exponentially small ripples at infinity},
url = {http://eudml.org/doc/78593},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Lombardi, E.
AU - Iooss, G.
TI - Gravity solitary waves with polynomial decay to exponentially small ripples at infinity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 4
SP - 669
EP - 704
LA - eng
KW - existence; analytic continuation; exponentially small upper bounds; oscillatory integrals
UR - http://eudml.org/doc/78593
ER -

References

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  3. [3] Benjamin T.B., Internal waves of permanent form in fluids of great depth, J. Fluid Mech.29 (1967) 559-592. Zbl0147.46502
  4. [4] Davis R.E., Acrivos A., Solitary internal waves in deep water, J. Fluid Mech.29 (1967) 593-607. Zbl0147.46503
  5. [5] F. Dias, G. Iooss, Water-Waves as a Spatial Dynamical System, Handbook of Mathematical Fluid Dynamics, to appear. Zbl1183.76630MR1984157
  6. [6] Iooss G., Gravity and capillary-gravity periodic travelling waves for two superposed fluid layers, one being of infinite depth, J. Math. Fluid Mech.1 (1999) 24-61. Zbl0926.76020MR1699018
  7. [7] Iooss G., Lombardi E., Sun S.M., Gravity travelling waves for two superposed fluid layers, one being of infinite depth: a new type of bifurcation, Phil. Trans. R. Soc. London A360 (2002) 2245-2336. Zbl1152.76335MR1949970
  8. [8] Levi-Civita T., Détermination rigoureuse des ondes permanentes d'ampleur finie, Math. Annalen93 (1925) 264-314. MR1512238JFM51.0671.06
  9. [9] Lombardi E., Orbits homoclinic to exponentially small periodic orbits for a class of reversible systems. Application to water waves, Arch. Rat. Mech. Anal.137 (1997) 227-304. Zbl0888.58039MR1463796
  10. [10] Lombardi E., Oscillatory Integrals and Phenomena Beyond all Algebraic Orders, with Applications to Homoclinic Orbits in Reversible Systems, Lecture Notes in Math., 1741, Springer, 2000. Zbl0959.34002MR1770093
  11. [11] Ono H., Algebraic solitary waves in stratified fluids, J. Phys. Soc. Japan39 (1975) 1082-1091. Zbl1334.76027MR398275
  12. [12] Părău E., Dias F., Interfacial periodic waves of permanent form with free-surface boundary conditions, J. Fluid Mech.437 (2001) 325-336. Zbl1054.76013MR1841797
  13. [13] Sun S.M., Shen M.C., Exponentially small estimate for the amplitude of capillary ripples of a generalized solitary wave, J. Math. Anal. Appl.172 (1993) 533-566. Zbl0772.76010MR1201004
  14. [14] Sun S.M., Existence of solitary internal waves in a two-layer fluid of infinite depth, Nonlinear Analysis30 (8) (1997) 5481-5490. Zbl0912.76013MR1726052
  15. [15] Sun S.M., Nonexistence of truly solitary waves in water with small surface tension, Proc. Roy. London A455 (1999) 2191-2228. Zbl0933.76014MR1702734

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