On Stokes waves and a conjecture of Levi-Civita;Sur les ondes de Stokes et une conjecture de Levi-Civita

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 326, Issue 11, 1998, Pages 1265-1268

  Buffoni, Boris ^a   Dancer, Edward Norman ^b   Toland, John Francis ^a  

^a University of Bath   (United Kingdom)

^b UNIVERSITY OF SYDNEY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032090787     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0764-4442(98)80176-6     Document Type: Article

References (11)

1. [1] Baesens C., MacKay R.S., Uniformly travelling water waves from a dynamical systems viewpoint: some insight into bifurcations from Stokes family, J. Fluid Mech. 241 (1992) 333-347.
2. [2] Buffoni B., Dancer E.N., Toland J.F., A variational theory of Stokes waves and their sub-harmonic bifurcations, prépublication (accessible anonymement par ftp.maths.bath.ac.uk:pub/preprints), 1998.
3. [3] Cushing J.M., On a conjecture of Levi-Civita, J. Math. Mech. 19 (1970) 1047-1050.
4. [4] Dancer E.N., Global structure of the solution set of non-linear real-analytic eigenvalue problems. Proc. Lond. Math. Soc. XXVI (1973) 359-384.
5. [5] Kielhöfer H., A bifurcation theorem for potential operators, J. Funct. Anal. 77 (1988) 1-8.
6. [6] Levi-Civita T., Détermination rigoureuse des ondes permanentes d'ampleur finie, Math. Ann. 93 (1925) 264-314.
7. [7] Lewy H., A note on harmonic functions and a hydrodynamic application, Proc. Amer. Math. Soc. 3 (1952) 111-113.
8. [8] Plotnikov P.I., Nonuniqueness of solutions of the problem of solitary waves and bifurcation of critical points of smooth functionals, Math. USSR Izv. 38 (2) (1992) 333-357.
9. [9] Saffman P.G., Long wavelength bifurcation of gravity waves on deep water, J. Fluid Mech. 101 (1980) 169-174.
10. [10] Stokes G.G., Considerations relative to the greatest height of oscillatory irrotational waves which can be propagated without change of form, Math. Phys. Papers, vol. I, Cambridge, 1880, pp. 225-228.
11. [11] Toland J.F., Stokes waves, Topol. Methods in Nonlin. Anal. 7-8 (1996-1997) 1-48 and 412-414.