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Volumn 1999, Issue 8, 1999, Pages

Large Time Behavior of Solutions for the Modified Korteweg-de Vries Equation

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EID: 0346390508     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (60)

References (32)
  • 1
    • 0003241821 scopus 로고
    • Solitons and the Inverse Scattering Transform
    • SIAM, Philadelphia
    • M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM Stud. Appl. Math. 4, SIAM, Philadelphia, 1981.
    • (1981) SIAM Stud. Appl. Math. , vol.4
    • Ablowitz, M.J.1    Segur, H.2
  • 2
    • 0038559361 scopus 로고
    • Dispersive blowup of solutions of generalized Korteweg-de Vries equations
    • J. L. Bona and J.-C. Saut, Dispersive blowup of solutions of generalized Korteweg-de Vries equations, J. Differential Equations 103 (1993), 3-57.
    • (1993) J. Differential Equations , vol.103 , pp. 3-57
    • Bona, J.L.1    Saut, J.-C.2
  • 3
    • 0002645561 scopus 로고
    • Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
    • F. M. Christ and M. I. Weinstein, Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal. 100 (1991), 87-109.
    • (1991) J. Funct. Anal. , vol.100 , pp. 87-109
    • Christ, F.M.1    Weinstein, M.I.2
  • 4
    • 84968508844 scopus 로고
    • Local smoothing properties of dispersive equations
    • P. Constantin and J.-C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988), 413-439.
    • (1988) J. Amer. Math. Soc. , vol.1 , pp. 413-439
    • Constantin, P.1    Saut, J.-C.2
  • 6
    • 85011573784 scopus 로고
    • Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
    • Non Linéaire
    • A. de Bouard, N. Hayashi, and K. Kato, Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995), 673-725.
    • (1995) Ann. Inst. H. Poincaré Anal , vol.12 , pp. 673-725
    • De Bouard, A.1    Hayashi, N.2    Kato, K.3
  • 7
    • 0001525213 scopus 로고
    • A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
    • P. Deift and X. Zhou, A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation, Ann. Math. 137 (1992), 295-368.
    • (1992) Ann. Math. , vol.137 , pp. 295-368
    • Deift, P.1    Zhou, X.2
  • 8
    • 17844377454 scopus 로고    scopus 로고
    • Long-time Behavior of Solutions of Linear Dispersive Equations
    • Springer, Berlin
    • D. B. Dix, Long-time Behavior of Solutions of Linear Dispersive Equations, Lecture Notes in Math. 1668, Springer, Berlin, 1997.
    • (1997) Lecture Notes in Math. , vol.1668
    • Dix, D.B.1
  • 10
    • 0042365657 scopus 로고    scopus 로고
    • Asymptotic Methods in Analysis
    • Springer-Verlag, New York
    • _, Asymptotic Methods in Analysis, Encyclopaedia Math. Sci. 13, Springer-Verlag, New York 1989.
    • Encyclopaedia Math. Sci. , vol.13 , pp. 1989
  • 12
    • 51249175708 scopus 로고
    • Existence and uniqueness of solutions for the generalized Korteweg-de Vries equation
    • J. Ginibre, Y. Tsutsumi, and G. Velo, Existence and uniqueness of solutions for the generalized Korteweg-de Vries equation, Math. Z. 203 (1990), 9-36.
    • (1990) Math. Z. , vol.203 , pp. 9-36
    • Ginibre, J.1    Tsutsumi, Y.2    Velo, G.3
  • 13
    • 0012812499 scopus 로고
    • Analyticity of solutions of the Korteweg-de Vries equation
    • N. Hayashi, Analyticity of solutions of the Korteweg-de Vries equation, SIAM J. Math. Anal. 22 (1991), 1738-1743.
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1738-1743
    • Hayashi, N.1
  • 14
    • 0031535503 scopus 로고    scopus 로고
    • Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation revisited
    • N. Hayashi and P. I. Naumkin, Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation revisited, Discrete Contin. Dynam. Systems 3 (1997), 383-400.
    • (1997) Discrete Contin. Dynam. Systems , vol.3 , pp. 383-400
    • Hayashi, N.1    Naumkin, P.I.2
  • 15
    • 0000462692 scopus 로고    scopus 로고
    • Asymptotics for large time of solutions to nonlinear Schrödinger and Hartree equations
    • _, Asymptotics for large time of solutions to nonlinear Schrödinger and Hartree equations, Amer. J. Math. 120 (1998), 369-389.
    • (1998) Amer. J. Math. , vol.120 , pp. 369-389
  • 16
    • 0007323978 scopus 로고    scopus 로고
    • Large time asymptotics of solutions to the generalized Korteweg-de Vries equation
    • _, Large time asymptotics of solutions to the generalized Korteweg-de Vries equation, J. Funct. Anal. 159 (1998), 110-136.
    • (1998) J. Funct. Anal. , vol.159 , pp. 110-136
  • 17
    • 22444453623 scopus 로고    scopus 로고
    • Large time asymptotics of solutions to the generalized Benjamin-Ono equation
    • _, Large time asymptotics of solutions to the generalized Benjamin-Ono equation, Trans. Amer. Math. Soc. 351 (1999), 109-130.
    • (1999) Trans. Amer. Math. Soc. , vol.351 , pp. 109-130
  • 18
    • 0002362136 scopus 로고
    • On the Cauchy problem for the (generalized) Korteweg-de Vries equation
    • Studies in Applied Mathematics, ed. V. Guillemin, Academic Press, New York
    • T. Kato, "On the Cauchy problem for the (generalized) Korteweg-de Vries equation" in Studies in Applied Mathematics, ed. V. Guillemin, Adv. Math. Supp. Stud. 8, Academic Press, New York, 1983, 93-128.
    • (1983) Adv. Math. Supp. Stud. , vol.8 , pp. 93-128
    • Kato, T.1
  • 19
    • 84972580144 scopus 로고
    • On the (generalized) Korteweg-de Vries equation
    • C. E. Kenig, G. Ponce, and L. Vega, On the (generalized) Korteweg-de Vries equation, Duke Math. J. 59 (1989), 585-610.
    • (1989) Duke Math. J. , vol.59 , pp. 585-610
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 20
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
    • _, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math. 46 (1993), 527-620.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 527-620
  • 21
    • 0002394348 scopus 로고
    • Long time behavior of solutions to nonlinear evolution equations
    • S. Klainerman, Long time behavior of solutions to nonlinear evolution equations, Arch. Rational Mech. Anal. 78 (1982), 73-98.
    • (1982) Arch. Rational Mech. Anal. , vol.78 , pp. 73-98
    • Klainerman, S.1
  • 22
    • 84990619712 scopus 로고
    • Global, small amplitude solutions to nonlinear evolution equations
    • S. Klainerman and G. Ponce, Global, small amplitude solutions to nonlinear evolution equations, Comm. Pure Appl. Math. 36 (1983), 133-141.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 133-141
    • Klainerman, S.1    Ponce, G.2
  • 23
    • 84956276540 scopus 로고
    • Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation
    • S. N. Kruzhkov and A. V. Faminskii, Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation, Math. USSR, Sbornik 48 (1984), 391-421.
    • (1984) Math. USSR, Sbornik , vol.48 , pp. 391-421
    • Kruzhkov, S.N.1    Faminskii, A.V.2
  • 24
    • 0347222392 scopus 로고    scopus 로고
    • Asymptotic behaviour as t → ∞ of solutions of the generalized Korteweg-de Vries equation
    • P. I. Naumkin and I. A. Shishmarev, Asymptotic behaviour as t → ∞ of solutions of the generalized Korteweg-de Vries equation, Mat. Sb. 187 (1996), 71-110.
    • (1996) Mat. Sb. , vol.187 , pp. 71-110
    • Naumkin, P.I.1    Shishmarev, I.A.2
  • 25
    • 0001631190 scopus 로고
    • Nonlinear small data scattering for the generalized Korteweg-de Vries equation
    • G. Ponce and L. Vega, Nonlinear small data scattering for the generalized Korteweg-de Vries equation, J. Funct. Anal. 90 (1990), 445-457.
    • (1990) J. Funct. Anal. , vol.90 , pp. 445-457
    • Ponce, G.1    Vega, L.2
  • 26
    • 0001857482 scopus 로고
    • Sur quelque généralisations de l'équation de Korteweg-de Vries
    • J.-C. Saut, Sur quelque généralisations de l'équation de Korteweg-de Vries, J. Math. Pure Appl. 58 (1979), 21-61.
    • (1979) J. Math. Pure Appl. , vol.58 , pp. 21-61
    • Saut, J.-C.1
  • 27
    • 0001152880 scopus 로고
    • Global existence of small solutions to nonlinear evolution equations
    • J. Shatah, Global existence of small solutions to nonlinear evolution equations, J. Differential Equations 46 (1982), 409-425.
    • (1982) J. Differential Equations , vol.46 , pp. 409-425
    • Shatah, J.1
  • 28
    • 0007076395 scopus 로고
    • On the long time behaviour of a generalized KdV equation
    • A. Sidi, C. Sulem, and P. L. Sulem, On the long time behaviour of a generalized KdV equation, Acta Appl. Math. 7 (1986), 35-47.
    • (1986) Acta Appl. Math. , vol.7 , pp. 35-47
    • Sidi, A.1    Sulem, C.2    Sulem, P.L.3
  • 29
    • 0347852485 scopus 로고    scopus 로고
    • On the generalized Korteweg-de Vries-type equations
    • G. Staffilani, On the generalized Korteweg-de Vries-type equations, Differential Integral Equations 10 (1997), 777-796.
    • (1997) Differential Integral Equations , vol.10 , pp. 777-796
    • Staffilani, G.1
  • 30
    • 0016334274 scopus 로고
    • Dispersion of low-energy waves for two conservative equations
    • W. A. Strauss, Dispersion of low-energy waves for two conservative equations, Arch. Rational Mech. Anal. 55 (1974), 86-92.
    • (1974) Arch. Rational Mech. Anal. , vol.55 , pp. 86-92
    • Strauss, W.A.1
  • 31
    • 0001684804 scopus 로고
    • Nonlinear scattering theory at low energy
    • _, Nonlinear scattering theory at low energy, J. Funct. Anal. 41 (1981), 110-133.
    • (1981) J. Funct. Anal. , vol.41 , pp. 110-133
  • 32
    • 85015856325 scopus 로고
    • On global solutions of the generalized Korteweg-de Vries equation
    • M. Tsutsumi, On global solutions of the generalized Korteweg-de Vries equation, Publ. Res. Inst. Math. Sci. 7 (1972), 329-344.
    • (1972) Publ. Res. Inst. Math. Sci. , vol.7 , pp. 329-344
    • Tsutsumi, M.1


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