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Volumn 146, Issue 3, 1999, Pages 183-220

A multiplicity result for solitary gravity-capillary waves in deep water via critical-point theory

(2)  Buffoni, B a   Groves, M D a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033466324     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050141     Document Type: Article
Times cited : (49)

References (38)
  • 2
    • 0001125277 scopus 로고
    • Multiplicité des orbites homoclines pour des systèmes conservatifs
    • AMBROSETTI, A. & COTI ZELATI, V., 1992, Multiplicité des orbites homoclines pour des systèmes conservatifs. C. R. Acad. Sci. Paris. 314, 601-604.
    • (1992) C. R. Acad. Sci. Paris , vol.314 , pp. 601-604
    • Ambrosetti, A.1    Coti Zelati, V.2
  • 3
    • 0002244618 scopus 로고
    • A theory of solitary water waves in the presence of surface tension
    • AMICK, C. J. & KIRCHGÄSSNER, K., 1989, A theory of solitary water waves in the presence of surface tension. Arch. Rational Mech. Anal. 105, 1-49.
    • (1989) Arch. Rational Mech. Anal. , vol.105 , pp. 1-49
    • Amick, C.J.1    Kirchgässner, K.2
  • 4
    • 0002157395 scopus 로고
    • A variational interpretation of Melnikov's function and exponentionally small separatrix splitting
    • ed. SALAMON, D. Cambridge Univ. Press.
    • ANGENENT, S., 1993, A variational interpretation of Melnikov's function and exponentionally small separatrix splitting. In Symplectic Geometry (ed. SALAMON, D.), pages 5-35. Cambridge Univ. Press.
    • (1993) Symplectic Geometry , pp. 5-35
    • Angenent, S.1
  • 5
    • 0027009632 scopus 로고
    • Uniformly travelling water waves from a dynamical systems viewpoint: Some insights into bifurcations from Stokes' family
    • BAESENS, C. & MACKAY, R. S., 1992, Uniformly travelling water waves from a dynamical systems viewpoint: some insights into bifurcations from Stokes' family. J. Fluid Mech. 241, 333-347.
    • (1992) J. Fluid Mech. , vol.241 , pp. 333-347
    • Baesens, C.1    MacKay, R.S.2
  • 6
    • 84990623719 scopus 로고
    • Solitary water waves with capillary ripples at infinity
    • BEALE, J. T., 1991, Solitary water waves with capillary ripples at infinity. Comm. Pure Appl. Math. 64, 211-257.
    • (1991) Comm. Pure Appl. Math. , vol.64 , pp. 211-257
    • Beale, J.T.1
  • 7
    • 0020292888 scopus 로고
    • Hamiltonian structure, symmetries and conservation laws for water waves
    • BENJAMIN, T. B. & OLVER, P. J. ,1982, Hamiltonian structure, symmetries and conservation laws for water waves. J. Fluid Mech. 125, 137-185.
    • (1982) J. Fluid Mech. , vol.125 , pp. 137-185
    • Benjamin, T.B.1    Olver, P.J.2
  • 8
    • 85012298299 scopus 로고
    • Homoclinic and period doubling bifurcations for damped systems
    • BESSI, U., 1995, Homoclinic and period doubling bifurcations for damped systems. Ann. Inst. Henri Poincaré Anal. Non Linéaire 12, 1-25.
    • (1995) Ann. Inst. Henri Poincaré Anal. Non Linéaire , vol.12 , pp. 1-25
    • Bessi, U.1
  • 10
    • 0027009769 scopus 로고
    • Spatial hamiltonian structure, energy flux and the water-wave problem
    • BRIDGES, T. J., 1992, Spatial hamiltonian structure, energy flux and the water-wave problem. Proc. Roy. Soc. Lond. A 439, 297-315.
    • (1992) Proc. Roy. Soc. Lond. A , vol.439 , pp. 297-315
    • Bridges, T.J.1
  • 11
    • 34249769656 scopus 로고
    • Hamiltonian spatial structure for three-dimensional water waves in a moving frame of reference
    • BRIDGES, T. J., 1994, Hamiltonian spatial structure for three-dimensional water waves in a moving frame of reference. J. Nonlinear Sci. 4, 221-251.
    • (1994) J. Nonlinear Sci. , vol.4 , pp. 221-251
    • Bridges, T.J.1
  • 12
    • 0012945442 scopus 로고
    • A proof of the Benjamin-Feir instability
    • BRIDGES, T. J. & MIELKE, A., 1995, A proof of the Benjamin-Feir instability. Arch. Rational Mech. Anal. 133, 145-198.
    • (1995) Arch. Rational Mech. Anal. , vol.133 , pp. 145-198
    • Bridges, T.J.1    Mielke, A.2
  • 13
    • 0043081376 scopus 로고    scopus 로고
    • A global condition for quasi-random behaviour in a class of conservative systems
    • BUFFONI, B. & SÉRÉ, E., 1996, A global condition for quasi-random behaviour in a class of conservative systems. Comm. Pure Appl. Math. 49, 285-305.
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 285-305
    • Buffoni, B.1    Séré, E.2
  • 14
    • 53349120754 scopus 로고    scopus 로고
    • Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system
    • BUFFONI, B., CHAMPNEYS, A. R. & TOLAND, J. F., 1996, Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system. J. Dynamics Diff. Eqns. 8, 221-279.
    • (1996) J. Dynamics Diff. Eqns. , vol.8 , pp. 221-279
    • Buffoni, B.1    Champneys, A.R.2    Toland, J.F.3
  • 15
    • 0029656885 scopus 로고    scopus 로고
    • A plethora of solitary gravity-capillary water waves with nearly critical bond and froude numbers
    • BUFFONI, B., GROVES, M. D. & TOLAND, J. F., 1996, A plethora of solitary gravity-capillary water waves with nearly critical Bond and Froude numbers. Phil. Trans. Roy. Soc. Lond. A 354, 575-607.
    • (1996) Phil. Trans. Roy. Soc. Lond. A , vol.354 , pp. 575-607
    • Buffoni, B.1    Groves, M.D.2    Toland, J.F.3
  • 17
    • 0000830631 scopus 로고
    • A variational approach to homoclinic orbits in Hamiltonian systems
    • COTI ZELATI, V., EKELAND, I. & SÉRÉ, E., 1990, A variational approach to homoclinic orbits in Hamiltonian systems. Math. Ann. 28, 133-160.
    • (1990) Math. Ann. , vol.28 , pp. 133-160
    • Coti Zelati, V.1    Ekeland, I.2    Séré, E.3
  • 18
    • 0000107832 scopus 로고
    • Homoclinic orbits in Hamiltonian systems
    • DEVANEY, R. L., 1976, Homoclinic orbits in Hamiltonian systems. J. Diff. Eqns. 21, 431-438.
    • (1976) J. Diff. Eqns. , vol.21 , pp. 431-438
    • Devaney, R.L.1
  • 19
    • 0000514133 scopus 로고
    • Capillary-gravity solitary waves with damped oscillations
    • DIAS, F. & IOOSS, G., 1993, Capillary-gravity solitary waves with damped oscillations. Physica D 65, 399-423.
    • (1993) Physica D , vol.65 , pp. 399-423
    • Dias, F.1    Iooss, G.2
  • 20
    • 0002232810 scopus 로고
    • A simple global characterization for normal forms of singular vector fields
    • ELPHICK, C., TIRAPEGUI, E., BRACHET, M. E., COULLET, P. & IOOSS, G., 1987, A simple global characterization for normal forms of singular vector fields. Physica D 29, 95-127.
    • (1987) Physica D , vol.29 , pp. 95-127
    • Elphick, C.1    Tirapegui, E.2    Brachet, M.E.3    Coullet, P.4    Iooss, G.5
  • 21
    • 0039436942 scopus 로고
    • A new Hamiltonian formulation of the steady water-wave problem
    • eds. MIELKE, A. & KIRCHGÄSSNER, K. Singapore: World Scientific
    • GROVES, M. D., 1995, A new Hamiltonian formulation of the steady water-wave problem. In Structure and Dynamics of Nonlinear Waves in Fluids (eds. MIELKE, A. & KIRCHGÄSSNER, K.), pages 259-267. Singapore: World Scientific.
    • (1995) Structure and Dynamics of Nonlinear Waves in Fluids , pp. 259-267
    • Groves, M.D.1
  • 22
    • 0031375381 scopus 로고    scopus 로고
    • On variational formulations for steady water waves
    • GROVES, M. D. & TOLAND, J. F., 1997, On variational formulations for steady water waves. Arch. Rational Mech. Anal. 137, 203-226.
    • (1997) Arch. Rational Mech. Anal. , vol.137 , pp. 203-226
    • Groves, M.D.1    Toland, J.F.2
  • 23
    • 84968468179 scopus 로고
    • A note on the topological degree at a critical point of mountainpass-type
    • HOFER, H., 1984, A note on the topological degree at a critical point of mountainpass-type. Proc. Amer. Math. Soc. 90, 309-315.
    • (1984) Proc. Amer. Math. Soc. , vol.90 , pp. 309-315
    • Hofer, H.1
  • 24
    • 0000594292 scopus 로고
    • Bifurcation d'ondes solitaires en présence d'une faible tension superficielle
    • IOOSS, G. & KIRCHGÄSSNER, K., 1990, Bifurcation d'ondes solitaires en présence d'une faible tension superficielle. C. R. Acad. Sci. Paris, Sér. 1 311, 265-268.
    • (1990) C. R. Acad. Sci. Paris, Sér. 1 , vol.311 , pp. 265-268
    • Iooss, G.1    Kirchgässner, K.2
  • 25
    • 0001933877 scopus 로고
    • Water waves for small surface tension: An approach via normal form
    • IOOSS, G. & KIRCHGÄSSNER, K., 1992, Water waves for small surface tension: an approach via normal form. Proc. Roy. Soc. Edin. A 122, 267-299.
    • (1992) Proc. Roy. Soc. Edin. A , vol.122 , pp. 267-299
    • Iooss, G.1    Kirchgässner, K.2
  • 26
    • 0039331554 scopus 로고    scopus 로고
    • Capillary gravity waves on the free surface of an inviscid fluid of infinite depth. Existence of solitary waves
    • IOOSS, G. & KIRRMANN, P., 1996, Capillary gravity waves on the free surface of an inviscid fluid of infinite depth. Existence of solitary waves. Arch. Rational Mech. Anal. 136, 1-19.
    • (1996) Arch. Rational Mech. Anal. , vol.136 , pp. 1-19
    • Iooss, G.1    Kirrmann, P.2
  • 27
    • 43949176143 scopus 로고
    • Perturbed homoclinic solutions in reversible 1:1 resonance vector fields
    • IOOSS, G. & PÉROUÈME, M. C., 1993, Perturbed homoclinic solutions in reversible 1:1 resonance vector fields. J. Diff. Eqns. 102, 62-88.
    • (1993) J. Diff. Eqns. , vol.102 , pp. 62-88
    • Iooss, G.1    Pérouème, M.C.2
  • 29
    • 0023702842 scopus 로고
    • Nonlinear resonant surface waves and homoclinic bifurcation
    • KIRCHGÄSSNER, K., 1988, Nonlinear resonant surface waves and homoclinic bifurcation. Adv. Appl. Math. 26, 135-181.
    • (1988) Adv. Appl. Math. , vol.26 , pp. 135-181
    • Kirchgässner, K.1
  • 30
    • 0031367392 scopus 로고    scopus 로고
    • Orbits homoclinic to exponentially small periodic orbits for a class of reversible systems. Application to water waves
    • LOMBARDI, E., 1997, Orbits homoclinic to exponentially small periodic orbits for a class of reversible systems. Application to water waves. Arch. Rational Mech. Anal. 137, 227-304.
    • (1997) Arch. Rational Mech. Anal. , vol.137 , pp. 227-304
    • Lombardi, E.1
  • 32
    • 0002801503 scopus 로고
    • Reduction of quasilinear elliptic equations in cylindrical domains with applications
    • MIELKE, A., 1988, Reduction of quasilinear elliptic equations in cylindrical domains with applications. Math. Meth. Appl. Sci. 10, 51-66.
    • (1988) Math. Meth. Appl. Sci. , vol.10 , pp. 51-66
    • Mielke, A.1
  • 34
    • 84974144443 scopus 로고
    • On Hamilton's principle for surface waves
    • MILES, J. W., 1977, On Hamilton's principle for surface waves. J. Fluid Mech. 83, 153-158.
    • (1977) J. Fluid Mech. , vol.83 , pp. 153-158
    • Miles, J.W.1
  • 35
    • 51249165518 scopus 로고
    • Existence of infinitely many homoclinic orbits in Hamiltoninan systems
    • SÉRÉ, E., 1992, Existence of infinitely many homoclinic orbits in Hamiltoninan systems. Math. Zeit. 209, 27-42.
    • (1992) Math. Zeit. , vol.209 , pp. 27-42
    • Séré, E.1
  • 36
    • 0000648116 scopus 로고
    • Existence of a generalized solitary wave solution for water waves with positive bond number less than 1/3
    • SUN, S. M., 1991, Existence of a generalized solitary wave solution for water waves with positive bond number less than 1/3. J. Math. Anal. Appl. 156, 533-566.
    • (1991) J. Math. Anal. Appl. , vol.156 , pp. 533-566
    • Sun, S.M.1
  • 37
    • 0001834355 scopus 로고
    • Stability of periodic waves of finite amplitude on the surface of a deep fluid
    • ZAKHAROV, V. E., 1968, Stability of periodic waves of finite amplitude on the surface of a deep fluid. Zh. Prikl. Mekh. Tekh. Fiz. 9, 86-94. (English translation J. Appl. Mech. Tech. Phys. 2, 190-194.)
    • (1968) Zh. Prikl. Mekh. Tekh. Fiz. , vol.9 , pp. 86-94
    • Zakharov, V.E.1
  • 38
    • 0007107074 scopus 로고    scopus 로고
    • English translation
    • ZAKHAROV, V. E., 1968, Stability of periodic waves of finite amplitude on the surface of a deep fluid. Zh. Prikl. Mekh. Tekh. Fiz. 9, 86-94. (English translation J. Appl. Mech. Tech. Phys. 2, 190-194.)
    • J. Appl. Mech. Tech. Phys. , vol.2 , pp. 190-194


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