Gravity solitary waves with polynomial decay to exponentially small ripples at infinity
Lombardi, E. ; Iooss, G.
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 669-704 / Harvested from Numdam
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@article{AIHPC_2003__20_4_669_0,
     author = {Lombardi, E. and Iooss, G\'erard},
     title = {Gravity solitary waves with polynomial decay to exponentially small ripples at infinity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {20},
     year = {2003},
     pages = {669-704},
     doi = {10.1016/S0294-1449(02)00023-9},
     mrnumber = {1981404},
     zbl = {1068.76008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_4_669_0}
}

Lombardi, E.; Iooss, G. Gravity solitary waves with polynomial decay to exponentially small ripples at infinity. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) pp. 669-704. doi : 10.1016/S0294-1449(02)00023-9. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_4_669_0/

[1] Amick C., On the theory of internal waves of permanent form in fluids of great depth, Trans. Amer. Math. Soc. 346 (1994) 399-419. | MR 1145726 | Zbl 0829.76012

[2] Amick C., Toland J., Uniqueness and related analytic properties for the Benjamin-Ono equation - a nonlinear Neumann problem in the plane, Acta Math. 167 (1991) 107-126. | MR 1111746 | Zbl 0755.35108

[3] Benjamin T.B., Internal waves of permanent form in fluids of great depth, J. Fluid Mech. 29 (1967) 559-592. | Zbl 0147.46502

[4] Davis R.E., Acrivos A., Solitary internal waves in deep water, J. Fluid Mech. 29 (1967) 593-607. | Zbl 0147.46503

[5] F. Dias, G. Iooss, Water-Waves as a Spatial Dynamical System, Handbook of Mathematical Fluid Dynamics, to appear. | MR 1984157 | Zbl 02019787

[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. | MR 1699018 | Zbl 0926.76020

[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 A 360 (2002) 2245-2336. | MR 1949970 | Zbl 01896123

[8] Levi-Civita T., Détermination rigoureuse des ondes permanentes d'ampleur finie, Math. Annalen 93 (1925) 264-314. | JFM 51.0671.06 | MR 1512238

[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. | MR 1463796 | Zbl 0888.58039

[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. | MR 1770093 | Zbl 0959.34002

[11] Ono H., Algebraic solitary waves in stratified fluids, J. Phys. Soc. Japan 39 (1975) 1082-1091. | MR 398275

[12] Părău E., Dias F., Interfacial periodic waves of permanent form with free-surface boundary conditions, J. Fluid Mech. 437 (2001) 325-336. | MR 1841797 | Zbl 1054.76013

[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. | MR 1201004 | Zbl 0772.76010

[14] Sun S.M., Existence of solitary internal waves in a two-layer fluid of infinite depth, Nonlinear Analysis 30 (8) (1997) 5481-5490. | MR 1726052 | Zbl 0912.76013

[15] Sun S.M., Nonexistence of truly solitary waves in water with small surface tension, Proc. Roy. London A 455 (1999) 2191-2228. | MR 1702734 | Zbl 0933.76014