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Volumn 31, Issue 1, 2002, Pages 69-91

Rigorous derivation of the nonlinear Schrödinger equation and Davey-Stewartson systems from quadratic hyperbolic systems

Author keywords

Davey Stewartson systems; Geometric optics; Nonlinear Schr dinger equation

Indexed keywords


EID: 0036660544     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (32)

References (33)
  • 1
    • 0042238449 scopus 로고    scopus 로고
    • Étude du système de Schrödinger-Bloch modèlisant la propagation d'un laser dans un gaz
    • R. Abarall, T. Colin and B. Nkonga, Étude du système de Schrödinger-Bloch modèlisant la propagation d'un laser dans un gaz, C. R. Acad. Sci. Sér. I 333(7) (2001), 689-692.
    • (2001) C. R. Acad. Sci. Sér. I , vol.333 , Issue.7 , pp. 689-692
    • Abarall, R.1    Colin, T.2    Nkonga, B.3
  • 4
    • 0029493020 scopus 로고
    • On rotational effects in the modulations of weakly nonlinear water waves over finite depth
    • T. Colin, F. Dias and J.-M. Ghidaglia, On rotational effects in the modulations of weakly nonlinear water waves over finite depth. European J. Mech. B Fluids 14(6) (1995), 775-793.
    • (1995) European J. Mech. B Fluids , vol.14 , Issue.6 , pp. 775-793
    • Colin, T.1    Dias, F.2    Ghidaglia, J.-M.3
  • 7
    • 0000541374 scopus 로고
    • On three-dimensional packets of surface waves
    • A. Davey and K. Stewartson, On three-dimensional packets of surface waves, Proc. Roy. Soc. London Ser. A 338 (1974), 101-110.
    • (1974) Proc. Roy. Soc. London Ser. A , vol.338 , pp. 101-110
    • Davey, A.1    Stewartson, K.2
  • 8
    • 0017471194 scopus 로고
    • On two-dimensional packets of capillary-gravity waves
    • V.D. Djorjevic and L.G. Redekopp, On two-dimensional packets of capillary-gravity waves, J Fluid Mech. 79 (1977), 703-714.
    • (1977) J Fluid Mech. , vol.79 , pp. 703-714
    • Djorjevic, V.D.1    Redekopp, L.G.2
  • 11
    • 0348090464 scopus 로고
    • On the initial value problem for the Davey-Stewartson systems
    • J.-M. Ghidaglia and J.-C. Saut, On the initial value problem for the Davey-Stewartson systems, Nonlinearity 9 (1990) 457-506.
    • (1990) Nonlinearity , vol.9 , pp. 457-506
    • Ghidaglia, J.-M.1    Saut, J.-C.2
  • 12
    • 0006649086 scopus 로고    scopus 로고
    • Sur une équation de Schrödinger non-linéaire avec interaction non-locale
    • Nonlinear Partial Differential Equations and Their Applications. H. Brezis and J.L. Lions, eds
    • J. Ginibre and G. Velo, Sur une équation de Schrödinger non-linéaire avec interaction non-locale, in: Nonlinear Partial Differential Equations and Their Applications. Collège de France Seminar, Vol. 2, H. Brezis and J.L. Lions, eds, Research Note in Math., Vol. 60, Pitman, 1982.
    • Collège de France Seminar , vol.2
    • Ginibre, J.1    Velo, G.2
  • 13
    • 0038893884 scopus 로고
    • Pitman
    • J. Ginibre and G. Velo, Sur une équation de Schrödinger non-linéaire avec interaction non-locale, in: Nonlinear Partial Differential Equations and Their Applications. Collège de France Seminar, Vol. 2, H. Brezis and J.L. Lions, eds, Research Note in Math., Vol. 60, Pitman, 1982.
    • (1982) Research Note in Math. , vol.60
  • 14
    • 0016461743 scopus 로고
    • The modulation and stability of an internal gravity wave
    • R. Grimshaw, The modulation and stability of an internal gravity wave, Mém. Soc. Roy. Sci. Liège, Sér. 6 X (1976) 299-314.
    • (1976) Mém. Soc. Roy. Sci. Liège, Sér. 6 , vol.10 , pp. 299-314
    • Grimshaw, R.1
  • 15
    • 0001822248 scopus 로고    scopus 로고
    • Local existence in time of small solutions to the elliptic-hyperbolic Davey-Stewartson system
    • N. Hayashi and H. Hirata, Local existence in time of small solutions to the elliptic-hyperbolic Davey-Stewartson system, Nonlinearity 9 (1996), 1387-1409.
    • (1996) Nonlinearity , vol.9 , pp. 1387-1409
    • Hayashi, N.1    Hirata, H.2
  • 16
    • 21844504284 scopus 로고
    • Focusing at a point and absorption of nonlinear oscillations
    • J.-L. Joly, G. Métivier and J. Rauch, Focusing at a point and absorption of nonlinear oscillations. Trans. Amer. Math. Soc. 347(10) (1995), 3921-3969.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , Issue.10 , pp. 3921-3969
    • Joly, J.-L.1    Métivier, G.2    Rauch, J.3
  • 17
    • 84974005262 scopus 로고
    • Generic rigorous asymptotic expansions for weakly nonlinear geometric optics
    • J.-L. Joly, G. Métivier and J. Rauch, Generic rigorous asymptotic expansions for weakly nonlinear geometric optics, Duke Math. J. 70 (1993), 373-404.
    • (1993) Duke Math. J. , vol.70 , pp. 373-404
    • Joly, J.-L.1    Métivier, G.2    Rauch, J.3
  • 18
    • 0002985997 scopus 로고
    • Coherent and focusing multidimensional nonlinear geometric optics
    • J.-L. Joly, G. Métivier and J. Rauch, Coherent and focusing multidimensional nonlinear geometric optics. Ann. Sci. École Norm. Sup. (4) 28(1) (1995), 51-113.
    • (1995) Ann. Sci. École Norm. Sup. (4) , vol.28 , Issue.1 , pp. 51-113
    • Joly, J.-L.1    Métivier, G.2    Rauch, J.3
  • 19
    • 0000954111 scopus 로고
    • Trilinear compensated compactness and nonlinear geometric optics
    • J.-L. Joly, G. Métivier and J. Rauch, Trilinear compensated compactness and nonlinear geometric optics, Ann. of Math. (2) 142(1) (1995), 121-169.
    • (1995) Ann. of Math. (2) , vol.142 , Issue.1 , pp. 121-169
    • Joly, J.-L.1    Métivier, G.2    Rauch, J.3
  • 20
    • 0001632163 scopus 로고    scopus 로고
    • Diffractive nonlinear geometric optics with rectification
    • J.-L. Joly, G. Métivier and J. Rauch, Diffractive nonlinear geometric optics with rectification, Indiana Univ. Math. J. 47(4) (1998), 1167-1241.
    • (1998) Indiana Univ. Math. J. , vol.47 , Issue.4 , pp. 1167-1241
    • Joly, J.-L.1    Métivier, G.2    Rauch, J.3
  • 21
    • 0034259179 scopus 로고    scopus 로고
    • Transparent nonlinear geometric optics and Maxwell-Bloch equations
    • J.-L. Joly, G. Métivier and J. Rauch, Transparent nonlinear geometric optics and Maxwell-Bloch equations, J. Differential Equations 166 (2000), 175-250.
    • (2000) J. Differential Equations , vol.166 , pp. 175-250
    • Joly, J.-L.1    Métivier, G.2    Rauch, J.3
  • 22
    • 0016428531 scopus 로고
    • Nonlinear self modulation of capillary-gravity waves on liquid layer
    • T. Kawahara, Nonlinear self modulation of capillary-gravity waves on liquid layer, J. Phys. Soc. Japan 38(1) (1975).
    • (1975) J. Phys. Soc. Japan , vol.38 , Issue.1
    • Kawahara, T.1
  • 23
    • 0001328731 scopus 로고    scopus 로고
    • Dispersive effects for nonlinear geometrical optics with rectification
    • D. Lannes, Dispersive effects for nonlinear geometrical optics with rectification, Asymptotic Anal. 18 (1998), 111-146.
    • (1998) Asymptotic Anal. , vol.18 , pp. 111-146
    • Lannes, D.1
  • 24
    • 0347460502 scopus 로고    scopus 로고
    • Thèse Université Bordeaux 1
    • D. Lannes, Thèse Université Bordeaux 1, 1999.
    • (1999)
    • Lannes, D.1
  • 25
    • 0009053006 scopus 로고    scopus 로고
    • Electromagnetic waves in ferrites: From linear absorption to the nonlinear Schrödinger equation
    • H. Leblond, Electromagnetic waves in ferrites: from linear absorption to the nonlinear Schrödinger equation, J. Phys. A 29(15) (1996), 4623-4639.
    • (1996) J. Phys. A , vol.29 , Issue.15 , pp. 4623-4639
    • Leblond, H.1
  • 26
    • 0033550139 scopus 로고    scopus 로고
    • Electromagnetic waves in ferromagnets: A Davey-Stewartson-type model
    • H. Leblond, Electromagnetic waves in ferromagnets: a Davey-Stewartson-type model, J. Phys. A 32(45) (1999), 7907-7932.
    • (1999) J. Phys. A , vol.32 , Issue.45 , pp. 7907-7932
    • Leblond, H.1
  • 27
    • 46549092797 scopus 로고
    • Hamiltonian approach to the description of nonlinear plasma phenomena
    • S.L. Musher, A.M. Rubenchick and V.E. Zakharov, Hamiltonian approach to the description of nonlinear plasma phenomena, Phys. Rep. 129(5) (1985), 285-366.
    • (1985) Phys. Rep. , vol.129 , Issue.5 , pp. 285-366
    • Musher, S.L.1    Rubenchick, A.M.2    Zakharov, V.E.3
  • 29
    • 21144463097 scopus 로고
    • A new type of soliton behavior in a two-dimensional plasma system
    • K. Nishinari, K. Abe and J. Satsuma, A new type of soliton behavior in a two-dimensional plasma system, J. Phys. Soc. Japan 62 (1993), 2021-2029.
    • (1993) J. Phys. Soc. Japan , vol.62 , pp. 2021-2029
    • Nishinari, K.1    Abe, K.2    Satsuma, J.3
  • 31
    • 0039500618 scopus 로고    scopus 로고
    • Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinaer equation
    • G. Schneider, Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinaer equation, J. Differential Equations 147(2) (1998), 333-354.
    • (1998) J. Differential Equations , vol.147 , Issue.2 , pp. 333-354
    • Schneider, G.1
  • 32
    • 0007015954 scopus 로고    scopus 로고
    • Justification of modulation equations for hyperbolic systems via normal forms
    • G. Schneider, Justification of modulation equations for hyperbolic systems via normal forms, Nonlinear Differential Equations Appl. 5(1) (1998), 69-82.
    • (1998) Nonlinear Differential Equations Appl. , vol.5 , Issue.1 , pp. 69-82
    • Schneider, G.1


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