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Volumn 360, Issue 1799, 2002, Pages 2245-2336

Gravity travelling waves for two superposed fluid layers, one being of infinite depth: A new type of bifurcation

Author keywords

Bifurcation theory; Homoclinic orbits; Infinite dimensional reversible dynamical systems; Nonlinear water waves; Normal forms with essential spectrum

Indexed keywords

WATER;

EID: 0037107541     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2002.1071     Document Type: Article
Times cited : (13)

References (21)
  • 1
    • 84968512861 scopus 로고
    • On the theory of internal waves of permanent form in fluids of great depth
    • Amick, C. 1994 On the theory of internal waves of permanent form in fluids of great depth. Trans. Am. Math. Soc. 346, 399-419.
    • (1994) Trans. Am. Math. Soc. , vol.346 , pp. 399-419
    • Amick, C.1
  • 2
    • 0002244618 scopus 로고
    • A theory of solitary water-waves in the presence of surface tension
    • Amick, C. & Kirchgässner, K. 1989 A theory of solitary water-waves in the presence of surface tension. Arch. Ration. Mech. Analysis 105, 1-49.
    • (1989) Arch. Ration. Mech. Analysis , vol.105 , pp. 1-49
    • Amick, C.1    Kirchgässner, K.2
  • 3
    • 0001533746 scopus 로고
    • Uniqueness and related analytic properties for the Benjamin-Ono equation - A nonlinear Neumann problem in the plane
    • Amick, C. & Toland, J. 1991 Uniqueness and related analytic properties for the Benjamin-Ono equation - A nonlinear Neumann problem in the plane. Acta Math. 167, 107-126.
    • (1991) Acta Math. , vol.167 , pp. 107-126
    • Amick, C.1    Toland, J.2
  • 4
    • 84902775564 scopus 로고
    • Internal waves of permanent form in fluids of great depth
    • Benjamin, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29, 559-592.
    • (1967) J. Fluid Mech. , vol.29 , pp. 559-592
    • Benjamin, T.B.1
  • 5
    • 77955587949 scopus 로고
    • Solitary internal waves in deep water
    • Davis, R. E. & Acrivos, A. 1967 Solitary internal waves in deep water. J. Fluid Mech. 29, 593-607.
    • (1967) J. Fluid Mech. , vol.29 , pp. 593-607
    • Davis, R.E.1    Acrivos, A.2
  • 6
    • 84995303671 scopus 로고    scopus 로고
    • Water-waves as a spatial dynamical system
    • (ed. S. Friedlander & D. Serre). Elsevier. (In the press.)
    • Dias, F. & Iooss, G. 2002 Water-waves as a spatial dynamical system. In Handbook of Mathematical Fluid Dynamics (ed. S. Friedlander & D. Serre). Elsevier. (In the press.)
    • (2002) Handbook of Mathematical Fluid Dynamics
    • Dias, F.1    Iooss, G.2
  • 7
    • 0002844243 scopus 로고    scopus 로고
    • Gravity and capillary-gravity periodic travelling waves for two superposed fluid layers, one being of infinite depth
    • Iooss, G. 1999 Gravity and capillary-gravity periodic travelling waves for two superposed fluid layers, one being of infinite depth. J. Math. Fluid Mech. 1, 24-61.
    • (1999) J. Math. Fluid Mech. , vol.1 , pp. 24-61
    • Iooss, G.1
  • 8
    • 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. I 311, 265-268.
    • (1990) C. R. Acad. Sci. Paris Sér. I , vol.311 , pp. 265-268
    • Iooss, G.1    Kirchgässner, K.2
  • 9
    • 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. Ration. Mech. Analysis 136, 1-19.
    • (1996) Arch. Ration. Mech. Analysis , vol.136 , pp. 1-19
    • Iooss, G.1    Kirrmann, P.2
  • 10
    • 43949176143 scopus 로고
    • Perturbed homoclinic solutions in 1:1 resonance vector fields
    • Iooss, G. & Pérouème, M. C. 1993 Perturbed homoclinic solutions in 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
  • 11
    • 0023702842 scopus 로고
    • Nonlinearly resonant surface waves and homoclinic bifurcation
    • Kirchgässner, K. 1988 Nonlinearly resonant surface waves and homoclinic bifurcation. Adv. Appl. Mech. 26, 135-181.
    • (1988) Adv. Appl. Mech. , vol.26 , pp. 135-181
    • Kirchgässner, K.1
  • 12
    • 0001647402 scopus 로고
    • Détermination rigoureuse des ondes permanentes d'ampleur finie
    • Levi-Civita, T. 1925 Détermination rigoureuse des ondes permanentes d'ampleur finie. Math. Annln 93, 264-314.
    • (1925) Math. Annln , vol.93 , pp. 264-314
    • Levi-Civita, T.1
  • 13
    • 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. Ration. Mech. Analysis 137, 227-304.
    • (1997) Arch. Ration. Mech. Analysis , vol.137 , pp. 227-304
    • Lombardi, E.1
  • 15
    • 0005162070 scopus 로고    scopus 로고
    • Gravity solitary waves with polynomial decay to exponentially small ripples at infinity
    • In the press
    • Lombardi, E. & Iooss, G. 2002 Gravity solitary waves with polynomial decay to exponentially small ripples at infinity. Annls Inst. H. Poincaré Analyse Non Linéaire. (In the press.)
    • (2002) Annls Inst. H. Poincaré Analyse Non Linéaire
    • Lombardi, E.1    Iooss, G.2
  • 16
    • 0002801503 scopus 로고
    • Reduction of quasilinear elliptic equation in cylindrical domains with applications
    • Mielke, A. 1988 Reduction of quasilinear elliptic equation 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
  • 17
    • 0016459710 scopus 로고
    • Algebraic solitary waves in stratified fluids
    • Ono, H. 1975 Algebraic solitary waves in stratified fluids. J. Phys. Soc. Jpn 39, 1082-1091.
    • (1975) J. Phys. Soc. Jpn. , vol.39 , pp. 1082-1091
    • Ono, H.1
  • 18
    • 0035948112 scopus 로고    scopus 로고
    • Interfacial periodic waves of permanent form with free-surface boundary conditions
    • Pǎrǎu, E. & Dias, F. 2001 Interfacial periodic waves of permanent form with free-surface boundary conditions. J. Fluid Mech. 437, 325-336.
    • (2001) J. Fluid Mech. , vol.437 , pp. 325-336
    • Pǎrǎu, E.1    Dias, F.2
  • 19
    • 0005158449 scopus 로고    scopus 로고
    • Existence of solitary internal waves in a two-layer fluid of infinite depth
    • Sun, S. M. 1997 Existence of solitary internal waves in a two-layer fluid of infinite depth. Nonlin. Analysis 30, 5481-5490.
    • (1997) Nonlin. Analysis , vol.30 , pp. 5481-5490
    • Sun, S.M.1
  • 20
    • 0001612930 scopus 로고    scopus 로고
    • Non existence of truly solitary waves in water with small surface tension
    • Sun, S. M. 1999 Non existence of truly solitary waves in water with small surface tension. Proc. R. Soc. Lond. A 455, 2191-2228.
    • (1999) Proc. R. Soc. Lond. A , vol.455 , pp. 2191-2228
    • Sun, S.M.1
  • 21
    • 0000606083 scopus 로고
    • Exponentially small estimate for the amplitude of capillary ripples of a generalized solitary wave
    • Sun, S. M. & Shen, M. C. 1993 Exponentially small estimate for the amplitude of capillary ripples of a generalized solitary wave. J. Math. Analysis Applic. 172, 533-566.
    • (1993) J. Math. Analysis Applic. , vol.172 , pp. 533-566
    • Sun, S.M.1    Shen, M.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.