메뉴 건너뛰기




Volumn 170, Issue 1, 2000, Pages 37-68

Lp-Lp Estimates for the Schrödinger Equation on the Line and Inverse Scattering for the Nonlinear Schrödinger Equation with a Potential

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0002283169     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3507     Document Type: Article
Times cited : (142)

References (38)
  • 3
    • 0003195954 scopus 로고
    • Schrödinger operators at thresholds
    • S. Albeverio, J. E. Fenstadt, H. Holden, & T. Lindstrøm. Cambridge: Cambridge Univ. Press
    • Bollé D. Schrödinger operators at thresholds. Albeverio S., Fenstadt J. E., Holden H., Lindstrøm T. Ideas and Methods in Quantum Statistical Physics. 1992;173-196 Cambridge Univ. Press, Cambridge.
    • (1992) Ideas and Methods in Quantum Statistical Physics , pp. 173-196
    • Bollé, D.1
  • 7
    • 0000109642 scopus 로고
    • Properties of the S matrix of the one-dimensional Schrödinger equation
    • Faddeev L. D. Properties of the S matrix of the one-dimensional Schrödinger equation. Trudy Mat. Inst. Steklov. 73:1964;314-333.
    • (1964) Trudy Mat. Inst. Steklov , vol.73 , pp. 314-333
    • Faddeev, L.D.1
  • 9
    • 49249148441 scopus 로고
    • On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
    • Ginibre J., Velo G. On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case. J. Funct. Anal. 32:1979;1-32.
    • (1979) J. Funct. Anal. , vol.32 , pp. 1-32
    • Ginibre, J.1    Velo, G.2
  • 10
    • 49249140378 scopus 로고
    • On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
    • Ginibre J., Velo G. On a class of nonlinear Schrödinger equations. II. Scattering theory, general case. J. Funct. Anal. 32:1979;33-71.
    • (1979) J. Funct. Anal. , vol.32 , pp. 33-71
    • Ginibre, J.1    Velo, G.2
  • 11
    • 0001274054 scopus 로고
    • On a class of nonlinear Schrödinger equations. III. Special theories in dimensions 1, 2, and 3
    • Ginibre J., Velo G. On a class of nonlinear Schrödinger equations. III. Special theories in dimensions 1, 2, and 3. Ann. Inst. H. Poincaré Phys. Théor. 28:1978;287-316.
    • (1978) Ann. Inst. H. Poincaré Phys. Théor. , vol.28 , pp. 287-316
    • Ginibre, J.1    Velo, G.2
  • 12
    • 0000205908 scopus 로고
    • Reconstruction of a potential on the line that is a priori known on the half-line
    • Grebert B., Weder R. Reconstruction of a potential on the line that is a priori known on the half-line. SIAM J. Appl. Math. 55:1995;242-254.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 242-254
    • Grebert, B.1    Weder, R.2
  • 15
    • 84972568716 scopus 로고
    • Spectral properties of Schrödinger operators and time-decay of the wave functions
    • Jensen A., Kato T. Spectral properties of Schrödinger operators and time-decay of the wave functions. Duke Math. J. 46:1979;583-611.
    • (1979) Duke Math. J. , vol.46 , pp. 583-611
    • Jensen, A.1    Kato, T.2
  • 18
    • 0000818765 scopus 로고
    • Nonlinear Schrödinger equations
    • H. Holden, & A. Jensen. Berlin: Springer-Verlag
    • Kato T. Nonlinear Schrödinger equations. Holden H., Jensen A. Schrödinger Operators. Lecture Notes in Physics. 345:1989;218-263 Springer-Verlag, Berlin.
    • (1989) Schrödinger Operators. Lecture Notes in Physics , vol.345 , pp. 218-263
    • Kato, T.1
  • 19
    • 0000959853 scopus 로고
    • Low-energy behaviour of the scattering matrix for the Schrödinger equation on the line
    • Klaus M. Low-energy behaviour of the scattering matrix for the Schrödinger equation on the line. Inverse Problems. 4:1988;505-512.
    • (1988) Inverse Problems , vol.4 , pp. 505-512
    • Klaus, M.1
  • 22
    • 0001608151 scopus 로고
    • Operator methods for inverse scattering on the real line
    • Melin A. Operator methods for inverse scattering on the real line. Comm. Partial Differential Equations. 10:1985;677-766.
    • (1985) Comm. Partial Differential Equations , vol.10 , pp. 677-766
    • Melin, A.1
  • 23
    • 0000936941 scopus 로고
    • Low-energy scattering for medium range potentials
    • Newton R. G. Low-energy scattering for medium range potentials. J. Math. Phys. 27:1986;2720-2730.
    • (1986) J. Math. Phys. , vol.27 , pp. 2720-2730
    • Newton, R.G.1
  • 25
    • 0004072884 scopus 로고
    • Lectures in Nonlinear Evolution Equations: Initial Value Problems
    • Braunschweig/Wiesbaden: Vieweg
    • Racke R. Lectures in Nonlinear Evolution Equations: Initial Value Problems. Aspects of Mathematics. E 19:1992;Vieweg, Braunschweig/Wiesbaden.
    • (1992) Aspects of Mathematics , vol.19
    • Racke, R.1
  • 29
    • 0001684804 scopus 로고
    • Nonlinear scattering theory at low energy
    • Strauss W. A. Nonlinear scattering theory at low energy. J. Funct. Anal. 41:1981;110-133.
    • (1981) J. Funct. Anal. , vol.41 , pp. 110-133
    • Strauss, W.A.1
  • 30
    • 0001684805 scopus 로고
    • Nonlinear scattering theory at low energy: Sequel
    • Strauss W. A. Nonlinear scattering theory at low energy: Sequel. J. Funct. Anal. 43:1981;281-293.
    • (1981) J. Funct. Anal. , vol.43 , pp. 281-293
    • Strauss, W.A.1
  • 31
    • 0003353148 scopus 로고
    • Nonlinear Wave Equations
    • Providence: Amer. Math. Soc.
    • Strauss W. A. Nonlinear Wave Equations. CBMS-RCSM. 73:1989;Amer. Math. Soc. Providence.
    • (1989) CBMS-RCSM , vol.73
    • Strauss, W.A.1
  • 32
    • 84972553620 scopus 로고
    • Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
    • Strichartz R. S. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44:1977;705-714.
    • (1977) Duke Math. J. , vol.44 , pp. 705-714
    • Strichartz, R.S.1
  • 33
    • 0001872603 scopus 로고    scopus 로고
    • Inverse scattering for the nonlinear Schrödinger equation
    • Weder R. 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
  • 34
    • 0002260691 scopus 로고
    • Spectral Theory of Ordinary Differential Operators
    • Berlin: Springer-Verlag
    • Weidmann J. Spectral Theory of Ordinary Differential Operators. Lecture Notes in Mathematics. 1258:1987;Springer-Verlag, Berlin.
    • (1987) Lecture Notes in Mathematics , vol.1258
    • Weidmann, J.1
  • 35
    • 0021538470 scopus 로고
    • Sound Propagation in Stratified Fluids
    • New York: Springer-Verlag
    • Wilcox C. H. Sound Propagation in Stratified Fluids. Applied Mathematical Sciences. 50:1984;Springer-Verlag, New York.
    • (1984) Applied Mathematical Sciences , vol.50
    • Wilcox, C.H.1
  • 36
    • 0002820736 scopus 로고
    • k, p-continuity of wave operators for Schrödinger operators
    • k, p-continuity of wave operators for Schrödinger operators. Proc. Japan Acad. Ser. A. 69:1993;94-98.
    • (1993) Proc. Japan Acad. Ser. a , vol.69 , pp. 94-98
    • Yajima, K.1
  • 37
    • 84972559697 scopus 로고
    • k, p-continuity of wave operators for Schrödinger operators
    • k, p-continuity of wave operators for Schrödinger operators. J. Math. Soc. Japan. 47:1995;551-581.
    • (1995) J. Math. Soc. Japan , vol.47 , pp. 551-581
    • Yajima, K.1
  • 38
    • 0009037488 scopus 로고
    • k, p-continuity of wave operators for Schrödinger operators. II. Positive potentials in even dimensions m≥4
    • M. Ikawa. New York: Dekker
    • k, p-continuity of wave operators for Schrödinger operators. II. Positive potentials in even dimensions m≥4. Ikawa M. Spectral and Scattering Theory. Lecture Notes in Pure and Applied Mathematics. 161:1994;287-300 Dekker, New York.
    • (1994) Spectral and Scattering Theory. Lecture Notes in Pure and Applied Mathematics , vol.161 , pp. 287-300
    • Yajima, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.