메뉴 건너뛰기




Volumn 54, Issue 5, 2002, Pages 1065-1085

Large time behavior for the cubic nonlinear Schrödinger equation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0036800092     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-2002-039-3     Document Type: Article
Times cited : (28)

References (23)
  • 1
    • 0002172263 scopus 로고
    • On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case; II Scattering theory, general case
    • J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case; II Scattering theory, general case. J. Funct. Anal. 32(1979), 1-71.
    • (1979) J. Funct. Anal. , vol.32 , pp. 1-71
    • Ginibre, J.1    Velo, G.2
  • 2
    • 0001632973 scopus 로고
    • Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension n ≤ 2
    • J. Ginibre and T. Ozawa, Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension n ≤ 2. Comm. Math. Phys. 151(1993), 619-645.
    • (1993) Comm. Math. Phys. , vol.151 , pp. 619-645
    • Ginibre, J.1    Ozawa, T.2
  • 3
    • 0001232403 scopus 로고
    • On the existence of wave operators for a class of nonlinear Schrödinger equations
    • J. Ginibre, T. Ozawa and G. Velo, On the existence of wave operators for a class of nonlinear Schrödinger equations. Ann. Inst. H. Poincaré Phys. Théor. 60(1994), 211-239.
    • (1994) Ann. Inst. H. Poincaré Phys. Théor. , vol.60 , pp. 211-239
    • Ginibre, J.1    Ozawa, T.2    Velo, G.3
  • 4
    • 0001729775 scopus 로고
    • The initial value problem for the derivative nonlinear Schrödinger equation in the energy space
    • N. Hayashi, The initial value problem for the derivative nonlinear Schrödinger equation in the energy space. Nonlinear Anal. 20(1993), 823-833.
    • (1993) Nonlinear Anal. , vol.20 , pp. 823-833
    • Hayashi, N.1
  • 5
    • 23044522241 scopus 로고    scopus 로고
    • Large time behavior of solutions to the dissipative nonlinear Schrödinger equation
    • N. Hayashi, E.I. Kaikina and P.I. Naumkin, Large time behavior of solutions to the dissipative nonlinear Schrödinger equation. Proc. Royal Soc. Edinburgh 130(2000), 1029-1043.
    • (2000) Proc. Royal Soc. Edinburgh , vol.130 , pp. 1029-1043
    • Hayashi, N.1    Kaikina, E.I.2    Naumkin, P.I.3
  • 6
    • 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
  • 7
    • 0000462692 scopus 로고    scopus 로고
    • Asymptotics in large time of solutions to nonlinear Schrödinger and Hartree equations
    • _, Asymptotics in 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
  • 8
    • 0002121786 scopus 로고    scopus 로고
    • Remarks on scattering theory and large time asymptotics of solutions to Hartree type equations with a long range potential
    • _, Remarks on scattering theory and large time asymptotics of solutions to Hartree type equations with a long range potential. SUT J. Math. 34(1998), 13-24.
    • (1998) SUT J. Math. , vol.34 , pp. 13-24
  • 9
    • 0000185063 scopus 로고    scopus 로고
    • Large time behavior of solutions for derivative cubic nonlinear Schrödinger equations without a self-conjugate property
    • _, Large time behavior of solutions for derivative cubic nonlinear Schrödinger equations without a self-conjugate property. Funkcial. Ekvac. 42(1999), 311-324.
    • (1999) Funkcial. Ekvac. , vol.42 , pp. 311-324
  • 10
    • 85036911241 scopus 로고    scopus 로고
    • Asymptotics of small solutions to nonlinear Schrödinger equations with cubic nonlinearities
    • to appear
    • _, Asymptotics of small solutions to nonlinear Schrödinger equations with cubic nonlinearities. Internat. J. Pure Appl. Math., to appear.
    • Internat. J. Pure Appl. Math.
  • 11
    • 84979545020 scopus 로고    scopus 로고
    • Large time behavior of solutions for derivative cubic nonlinear Schrödinger equations
    • N. Hayashi, P.I. Naumkin and H. Uchida, Large time behavior of solutions for derivative cubic nonlinear Schrödinger equations. Publ. Res. Inst. Math. Sci. 35(1999), 501-513.
    • (1999) Publ. Res. Inst. Math. Sci. , vol.35 , pp. 501-513
    • Hayashi, N.1    Naumkin, P.I.2    Uchida, H.3
  • 12
    • 0000872655 scopus 로고
    • Modified wave operators for the derivative nonlinear Schrödinger equation
    • N. Hayashi and T. Ozawa, Modified wave operators for the derivative nonlinear Schrödinger equation. Math. Ann. 298(1994), 557-576.
    • (1994) Math. Ann. , vol.298 , pp. 557-576
    • Hayashi, N.1    Ozawa, T.2
  • 13
    • 84972525950 scopus 로고
    • Remarks on nonlinear Schrödinger equations in one space dimension
    • _, Remarks on nonlinear Schrödinger equations in one space dimension. Differential Integral Equations 7(1994), 453-461.
    • (1994) Differential Integral Equations , vol.7 , pp. 453-461
  • 14
    • 0001394681 scopus 로고
    • Global existence of solutions for nonlinear Schrödinger equations in one space dimension
    • S. Katayama and Y. Tsutsumi, Global existence of solutions for nonlinear Schrödinger equations in one space dimension. Comm. Partial Differential Equations 19(1994), 1971-1997.
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 1971-1997
    • Katayama, S.1    Tsutsumi, Y.2
  • 15
    • 36749109491 scopus 로고
    • An exact solution for a derivative nonlinear Schrödinger equation
    • D.J. Kaup and A.C. Newell, An exact solution for a derivative nonlinear Schrödinger equation. J. Math. Phys. 19(1978), 789-801.
    • (1978) J. Math. Phys. , vol.19 , pp. 789-801
    • Kaup, D.J.1    Newell, A.C.2
  • 16
    • 0016972663 scopus 로고
    • Modified nonlinear Schrödinger equation for Alfven waves propagating along the magnetic field in cold plasmas
    • W. Mio, T. Ogino, K. Minami and S. Takeda, Modified nonlinear Schrödinger equation for Alfven waves propagating along the magnetic field in cold plasmas. J. Phys. Soc. Japan 41(1976), 265-271.
    • (1976) J. Phys. Soc. Japan , vol.41 , pp. 265-271
    • Mio, W.1    Ogino, T.2    Minami, K.3    Takeda, S.4
  • 17
    • 0017216310 scopus 로고
    • On the modulation instability of hydromagnetic waves parallel to the magnetic field parallel to the magnetic field
    • E. Mjølhus, On the modulation instability of hydromagnetic waves parallel to the magnetic field parallel to the magnetic field. J. Plasma Phys. 16(1976), 321-334.
    • (1976) J. Plasma Phys. , vol.16 , pp. 321-334
    • Mjølhus, E.1
  • 18
    • 0010969692 scopus 로고    scopus 로고
    • Cubic derivative nonlinear Schrödinger equations
    • P.I. Naumkin, Cubic derivative nonlinear Schrödinger equations. SUT J. Math. 36(2000), 9-42.
    • (2000) SUT J. Math. , vol.36 , pp. 9-42
    • Naumkin, P.I.1
  • 19
    • 0003001402 scopus 로고    scopus 로고
    • On the nonlinear Schrödinger equations of derivative type
    • T. Ozawa, On the nonlinear Schrödinger equations of derivative type. Indiana Univ. Math. J. 45(1996), 137-163.
    • (1996) Indiana Univ. Math. J. , vol.45 , pp. 137-163
    • Ozawa, T.1
  • 20
    • 0001366166 scopus 로고
    • Long range scattering for nonlinear Schrödinger equations in one space dimension
    • _, Long range scattering for nonlinear Schrödinger equations in one space dimension. Comm. Math. Phys. 139(1991), 479-493.
    • (1991) Comm. Math. Phys. , vol.139 , pp. 479-493
  • 21
    • 84990623722 scopus 로고
    • Normal forms and quadratic nonlinear Klein-Gordon equations
    • J. Shatah, Normal forms and quadratic nonlinear Klein-Gordon equations. Comm. Pure Appl. Math. 38(1985), 685-696.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 685-696
    • Shatah, J.1
  • 22
    • 84979589173 scopus 로고    scopus 로고
    • Global existence for a class of cubic nonlinear Schrödinger equations in one space dimension
    • S. Tonegawa, Global existence for a class of cubic nonlinear Schrödinger equations in one space dimension. Hokkaido Math. J. 30(2001), 451-473.
    • (2001) Hokkaido Math. J. , vol.30 , pp. 451-473
    • Tonegawa, S.1
  • 23
    • 0010972209 scopus 로고
    • The null gauge condition and the one dimensional nonlinear Schrödinger equation with cubic nonlinearity
    • Y. Tsutsumi, The null gauge condition and the one dimensional nonlinear Schrödinger equation with cubic nonlinearity. Indiana Univ. Math. J. 44(1994), 241-254.
    • (1994) Indiana Univ. Math. J. , vol.44 , pp. 241-254
    • Tsutsumi, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.