# Existence by minimisation of solitary water waves on an ocean of infinite depth

Annales de l'I.H.P. Analyse non linéaire (2004)

- Volume: 21, Issue: 4, page 503-516
- ISSN: 0294-1449

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topBuffoni, B. "Existence by minimisation of solitary water waves on an ocean of infinite depth." Annales de l'I.H.P. Analyse non linéaire 21.4 (2004): 503-516. <http://eudml.org/doc/78627>.

@article{Buffoni2004,

author = {Buffoni, B},

journal = {Annales de l'I.H.P. Analyse non linéaire},

keywords = {Capillary-gravity water waves; solitary waves; variational methods},

language = {eng},

number = {4},

pages = {503-516},

publisher = {Elsevier},

title = {Existence by minimisation of solitary water waves on an ocean of infinite depth},

url = {http://eudml.org/doc/78627},

volume = {21},

year = {2004},

}

TY - JOUR

AU - Buffoni, B

TI - Existence by minimisation of solitary water waves on an ocean of infinite depth

JO - Annales de l'I.H.P. Analyse non linéaire

PY - 2004

PB - Elsevier

VL - 21

IS - 4

SP - 503

EP - 516

LA - eng

KW - Capillary-gravity water waves; solitary waves; variational methods

UR - http://eudml.org/doc/78627

ER -

## References

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- [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. Zbl0641.76008MR899856
- [3] B. Buffoni, Existence and conditional energetic stability of capillary-gravity solitary water waves by minimisation, preprint. Zbl1110.76308MR2073504
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- [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. Zbl1222.76019
- [6] B. Buffoni, É. Séré, J.F. Toland, Minimisation methods for quasi-linear problems, with an application to periodic water waves, preprint. Zbl1077.76058MR2139201
- [7] Garabedian P.R, Surface waves of finite depth, J. Anal. Math.14 (1965) 161-169. Zbl0128.44502MR184511
- [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. Zbl0879.76011MR1423002
- [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. Zbl0507.44006MR688574
- [10] Stuart C.A, Bifurcation into Spectral Gaps, Bull. Belg. Math. Soc. Simon Stevin, 1995. Zbl0864.47037MR1361485
- [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. Zbl0888.47045MR1453894
- [12] Turner R.E.L, A variational approach to surface solitary waves, J. Differential Equations55 (1984) 401-438. Zbl0574.76015MR766131
- [13] Zygmund A, Trigonometric Series I, II, Cambridge University Press, Cambridge, 1959. Zbl0367.42001MR107776

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