Existence by minimisation of solitary water waves on an ocean of infinite depth
Annales de l'I.H.P. Analyse non linéaire, Volume 21 (2004) no. 4, p. 503-516
@article{AIHPC_2004__21_4_503_0,
author = {Buffoni, Boris},
title = {Existence by minimisation of solitary water waves on an ocean of infinite depth},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {21},
number = {4},
year = {2004},
pages = {503-516},
doi = {10.1016/j.anihpc.2003.06.003},
zbl = {1109.76013},
mrnumber = {2069635},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2004__21_4_503_0}
}

Buffoni, B. Existence by minimisation of solitary water waves on an ocean of infinite depth. Annales de l'I.H.P. Analyse non linéaire, Volume 21 (2004) no. 4, pp. 503-516. doi : 10.1016/j.anihpc.2003.06.003. http://www.numdam.org/item/AIHPC_2004__21_4_503_0/

[1] Babenko K.I, Some remarks on the theory of surface waves of finite amplitude, Soviet Math. Dokl. 35 (1987) 599-603. | MR 898306 | Zbl 0641.76007

[2] Babenko K.I, On a local existence theorem in the theory of surface waves of finite amplitude, Soviet Math. Dokl. 35 (1987) 647-650. | MR 899856 | Zbl 0641.76008

[3] B. Buffoni, Existence and conditional energetic stability of capillary-gravity solitary water waves by minimisation, preprint. | MR 2073504

[4] Buffoni B, Dancer E.N, Toland J.F, The regularity and local bifurcation of steady periodic water waves, Arch. Rational Mech. Anal. 152 (2000) 207-240. | MR 1764945 | Zbl 0959.76010

[5] B. Buffoni, É. Séré, J.F. Toland, Surface water waves as saddle points of the energy, Calculus of Variations and Partial Differential Equations, submitted for publication. | Zbl 01969058

[6] B. Buffoni, É. Séré, J.F. Toland, Minimisation methods for quasi-linear problems, with an application to periodic water waves, preprint. | MR 2139201

[7] Garabedian P.R, Surface waves of finite depth, J. Anal. Math. 14 (1965) 161-169. | MR 184511 | Zbl 0128.44502

[8] Iooss G, Kirrmann P, Capillary gravity waves on the free surface of an inviscid fluid of infinite depth, Existence of solitary waves, Arch. Rational Mech. Anal. 136 (1998) 1-19. | MR 1423002 | Zbl 0879.76011

[9] Logan B.F, Hilbert transform of a function having a bounded integral and a bounded derivative, SIAM J. Math. Anal. 14 (1983) 247-248. | MR 688574 | Zbl 0507.44006

[10] Stuart C.A, Bifurcation into Spectral Gaps, Bull. Belg. Math. Soc. Simon Stevin, 1995. | MR 1361485 | Zbl 0864.47037

[11] Stuart C.A, Bifurcation from the essential spectrum, in: Topological Nonlinear Analysis II (Frascati, 1995), Progr. Nonlinear Differential Equations Appl., vol. 27, Birkhäuser, Boston, 1997, pp. 397-443. | MR 1453894 | Zbl 0888.47045

[12] Turner R.E.L, A variational approach to surface solitary waves, J. Differential Equations 55 (1984) 401-438. | MR 766131 | Zbl 0574.76015

[13] Zygmund A, Trigonometric Series I, II, Cambridge University Press, Cambridge, 1959. | MR 107776 | Zbl 0367.42001