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Volumn 184, Issue 1, 2002, Pages 62-77

Multidimensional inverse scattering for the nonlinear Klein-Gordon equation with a potential

Author keywords

Inverse scattering; Nonlinear equations

Indexed keywords


EID: 0036747937     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2001.4133     Document Type: Article
Times cited : (30)

References (25)
  • 1
    • 85031388906 scopus 로고
    • "Sobolev Spaces"
    • Academic Press, New York
    • R. A. Adams, "Sobolev Spaces," Academic Press, New York, 1975.
    • (1975)
    • Adams, R.A.1
  • 2
    • 0000817005 scopus 로고
    • Problème inverse de diffusion non linéaire
    • A. Bachelot, Problème inverse de diffusion non linéaire, C. R. Acad. Sci. Paris Sér. I 293 (1981), 121-124.
    • (1981) C. R. Acad. Sci. Paris Sér. I , vol.293 , pp. 121-124
    • Bachelot, A.1
  • 3
    • 0002598095 scopus 로고
    • n+1) de la solution de l'équation de Klein-Gordon vers celle de l'équation des ondes
    • n+1) de la solution de l'équation de Klein-Gordon vers celle de l'équation des ondes, Ann. Fac. Sci. Toulouse VIII (1987), 37-60.
    • (1987) Ann. Fac. Sci. Toulouse , vol.8 , pp. 37-60
    • Bachelot, A.1
  • 4
    • 85031380700 scopus 로고    scopus 로고
    • Deleted in proof
    • Deleted in proof.
  • 5
    • 21844495844 scopus 로고
    • The geometrical approach to multidimensional inverse scattering
    • V. Enss and R. Weder, The geometrical approach to multidimensional inverse scattering, J. Math. Phys. 36 (1995), 3902-3921.
    • (1995) J. Math. Phys , vol.36 , pp. 3902-3921
    • Enss, V.1    Weder, R.2
  • 6
    • 33846118011 scopus 로고
    • Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators
    • R. Froese and I. Herbst, Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators, Comm. Math. Phys. 87 (1982/83), 429-447.
    • (1982) Comm. Math. Phys , vol.87 , pp. 429-447
    • Froese, R.1    Herbst, I.2
  • 7
    • 0000818765 scopus 로고
    • Nonlinear Schrödinger equations
    • (H. Holden and A. Jensen, Eds.), Lecture Notes in Physics, Springer-Verlag, Berlin
    • T. Kato, Nonlinear Schrödinger equations, in "Schrödinger Operators," (H. Holden and A. Jensen, Eds.), pp. 218-263, Lecture Notes in Physics, Vol. 345, Springer-Verlag, Berlin, 1989.
    • (1989) "Schrödinger Operators" , vol.345 , pp. 218-263
    • Kato, T.1
  • 9
    • 0003604020 scopus 로고
    • "Notes in Time Decay and Scattering for Some Hyperbolic Problems"
    • Regional Series in Applied Mathematics, SIAM, Philadelphia, PA
    • C. Morawetz, "Notes in Time Decay and Scattering for Some Hyperbolic Problems," Regional Series in Applied Mathematics, SIAM, Philadelphia, PA, 1975.
    • (1975)
    • Morawetz, C.1
  • 10
  • 11
    • 0003687441 scopus 로고
    • "Methods of Modern Mathematical Physics I: Functional Analysis"
    • Academic Press, New York
    • M. Reed and B. Simon, "Methods of Modern Mathematical Physics I: Functional Analysis," Academic Press, New York, 1972.
    • (1972)
    • Reed, M.1    Simon, B.2
  • 12
    • 85031387967 scopus 로고    scopus 로고
    • Deleted in proof
    • Deleted in proof.
  • 13
    • 0003937747 scopus 로고
    • "Methods of Modern Mathematical Physics III: Scattering Theory"
    • Academic Press, New York
    • M. Reed and B. Simon, "Methods of Modern Mathematical Physics III: Scattering Theory," Academic Press, New York, 1978.
    • (1978)
    • Reed, M.1    Simon, B.2
  • 15
    • 0003799686 scopus 로고
    • "Singular Integrals and Differentiability Properties of Functions"
    • Princeton Univ. Press, Princeton, NJ
    • E. M. Stein, "Singular Integrals and Differentiability Properties of Functions," Princeton Univ. Press, Princeton, NJ, 1970.
    • (1970)
    • Stein, E.M.1
  • 16
    • 85031369277 scopus 로고    scopus 로고
    • Deleted in proof
    • Deleted in proof.
  • 17
    • 0001872603 scopus 로고    scopus 로고
    • Inverse scattering for the nonlinear Schrödinger equation
    • R. Weder, Inverse scattering for the nonlinear Schrödinger equation, Comm. Partial Differential Equations 22 (1997), 2089-2103.
    • (1997) Comm. Partial Differential Equations , vol.22 , pp. 2089-2103
    • Weder, R.1
  • 18
    • 0033235140 scopus 로고    scopus 로고
    • k,p-continuity of the Schrödinger wave operators on the line
    • k,p-continuity of the Schrödinger wave operators on the line, Comm. Math. Phys. 208 (1999), 507-520.
    • (1999) Comm. Math. Phys , vol.208 , pp. 507-520
    • Weder, R.1
  • 19
    • 0002283169 scopus 로고    scopus 로고
    • p estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
    • p estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential, J. Funct. Anal. 170 (2000), 37-68.
    • (2000) J. Funct. Anal , vol.170 , pp. 37-68
    • Weder, R.1
  • 20
    • 0034410054 scopus 로고    scopus 로고
    • Inverse scattering on the line for the nonlinear Klein-Gordon equation with a potential
    • R. Weder, Inverse scattering on the line for the nonlinear Klein-Gordon equation with a potential, J. Math. Anal. Appl. 252 (2000), 102-123.
    • (2000) J. Math. Anal. Appl , vol.252 , pp. 102-123
    • Weder, R.1
  • 21
    • 0034831729 scopus 로고    scopus 로고
    • Inverse scattering for the nonlinear Schrödinger equation. Reconstruction of the potential and the nonlinearity
    • R. Weder, Inverse scattering for the nonlinear Schrödinger equation. Reconstruction of the potential and the nonlinearity, Math. Methods Appl. Sci. 24 (2001), 245-254.
    • (2001) Math. Methods Appl. Sci , vol.24 , pp. 245-254
    • Weder, R.1
  • 22
    • 23044531521 scopus 로고    scopus 로고
    • Inverse scattering for the nonlinear Schrödinger equation II. Reconstruction of the potential and the nonlinearity in the multidimensional case
    • R. Weder, Inverse scattering for the nonlinear Schrödinger equation II. Reconstruction of the potential and the nonlinearity in the multidimensional case, Proc. Amer. Math. Soc. 129 (2001), 3637-3645.
    • (2001) Proc. Amer. Math. Soc , vol.129 , pp. 3637-3645
    • Weder, R.1
  • 23
    • 84972559697 scopus 로고
    • k,p-continuity of the wave operators for Schrödinger operators
    • k,p-continuity of the wave operators for Schrödinger operators, J. Math. Soc. Japan 47 (1995), 552-581.
    • (1995) J. Math. Soc. Japan , vol.47 , pp. 552-581
    • Yajima, K.1
  • 24
    • 0001604108 scopus 로고
    • k,p-continuity of the wave operators for Schrödinger operators III, even dimensional cases m≥4
    • k,p-continuity of the wave operators for Schrödinger operators III, even dimensional cases m≥4, J. Math. Sci. Univ. Tokyo 2 (1995), 311-346.
    • (1995) J. Math. Sci. Univ. Tokyo , vol.2 , pp. 311-346
    • Yajima, K.1
  • 25
    • 0033235580 scopus 로고    scopus 로고
    • p-boundedness of wave operators for two dimensional Schrödinger operators
    • p-boundedness of wave operators for two dimensional Schrödinger operators, Comm. Math. Phys. 208 (1999),
    • (1999) Comm. Math. Phys , vol.208 , pp. 125-152
    • Yajima, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.