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Volumn 39, Issue 37, 2006, Pages 11461-11478

The initial value problem, scattering and inverse scattering, for Schrödinger equations with a potential and a non-local nonlinearity

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EID: 33748329587     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/37/009     Document Type: Article
Times cited : (6)

References (52)
  • 1
    • 0041738945 scopus 로고    scopus 로고
    • A class of nonlinear Schrödinger equations with concentrated nonlinearities
    • Adami R and Teta A 2001 A class of nonlinear Schrödinger equations with concentrated nonlinearities J. Funct. Anal. 180 148-75
    • (2001) J. Funct. Anal. , vol.180 , Issue.1 , pp. 148-175
    • Adami, R.1    Teta, A.2
  • 2
    • 84858939986 scopus 로고    scopus 로고
    • Blow-up for Schrödinger equations with pointwise nonlinearity
    • Adami R 2002 Blow-up for Schrödinger equations with pointwise nonlinearity Mathematical Methods in Quantum Mechanics (Contemporary Mathematics vol 307) ed R Weder, P Exner and B Grébert (Providence, RI: American Mathematical Society) pp 1-7
    • (2002) Mathematical Methods in Quantum Mechanics , pp. 1-7
    • Adami, R.1
  • 3
    • 0347354930 scopus 로고    scopus 로고
    • The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity
    • Adami R, Dell'Antonio G, Figari R and Teta A 2003 The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity Ann. Inst. H. Poincaré Anal. Non Linéaire 20 477-500
    • (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.20 , pp. 477-500
    • Adami, R.1    Dell'Antonio, G.2    Figari, R.3    Teta, A.4
  • 4
    • 0842265107 scopus 로고    scopus 로고
    • Blow up solutions for the Schrödinger equation in dimension three with concentrated nonlinearity
    • Adami R, Dell'Antonio G, Figari R and Teta A 2004 Blow up solutions for the Schrödinger equation in dimension three with concentrated nonlinearity Ann. Inst. H. Poincaré Anal. Non Linéaire 21 121-37
    • (2004) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.21 , Issue.1 , pp. 121-137
    • Adami, R.1    Dell'Antonio, G.2    Figari, R.3    Teta, A.4
  • 6
    • 0005717398 scopus 로고    scopus 로고
    • Inverse theory: Problem on the line
    • Aktosun T and Klaus M 2002 Inverse theory: problem on the line Scattering vol 1 ed R Pike and P Sabatier (New York: Academic) pp 770-85
    • (2002) Scattering , vol.1 , pp. 770-785
    • Aktosun, T.1    Klaus, M.2
  • 10
    • 0002536782 scopus 로고
    • Symmetry breaking for a nonlinear Schrödinger operator
    • Davies E B 1979 Symmetry breaking for a nonlinear Schrödinger operator Commun. Math. Phys. 64 191-210
    • (1979) Commun. Math. Phys. , vol.64 , Issue.3 , pp. 191-210
    • Davies, E.B.1
  • 11
    • 21844489409 scopus 로고
    • Nonlinear Schrödinger operator and molecular structure
    • Davies E B 1995 Nonlinear Schrödinger operator and molecular structure J. Phys. A: Math. Gen. 28 4025-41
    • (1995) J. Phys. A: Math. Gen. , vol.28 , Issue.14 , pp. 4025-4041
    • Davies, E.B.1
  • 13
    • 0000109642 scopus 로고
    • Properties of the S matrix of the one-dimensional Schrödinger equation
    • Faddeev L D 1964 Properties of the S matrix of the one-dimensional Schrödinger equation Trudy Math. Inst. Steklov 73 314-33
    • (1964) Trudy Math. Inst. Steklov , vol.73 , pp. 314-333
    • Faddeev, L.D.1
  • 18
    • 21844506769 scopus 로고
    • Non linear Stark effect and molecular localization
    • Grecchi V and Martinez A 1995 Non linear Stark effect and molecular localization Commun. Math. Phys. 166 533-48
    • (1995) Commun. Math. Phys. , vol.166 , Issue.3 , pp. 533-548
    • Grecchi, V.1    Martinez, A.2
  • 19
    • 0036591107 scopus 로고    scopus 로고
    • Destruction of the beating effect for a nonlinear Schrödinger equation
    • Grecchi V, Martinez A and Sachetti A 2002 Destruction of the beating effect for a nonlinear Schrödinger equation Commun. Math. Phys. 227 191-209
    • (2002) Commun. Math. Phys. , vol.227 , Issue.1 , pp. 191-209
    • Grecchi, V.1    Martinez, A.2    Sachetti, A.3
  • 20
    • 0000683218 scopus 로고
    • Chaotic quantum phenomena without classical counterpart
    • Jona-Lasinio G, Presilla C and Capasso F 1992 Chaotic quantum phenomena without classical counterpart Phys. Rev. Lett. 68 2269-72
    • (1992) Phys. Rev. Lett. , vol.68 , Issue.15 , pp. 2269-2272
    • Jona-Lasinio, G.1    Presilla, C.2    Capasso, F.3
  • 21
    • 84858930863 scopus 로고
    • Stationary solutions and invariant tori for a class of nonlinear non-local Schrödinger equations
    • Jona-Lasinio G 1995 Stationary solutions and invariant tori for a class of nonlinear non-local Schrödinger equations Advances in Dynamical Systems and Quantum Physics (River Edge, NJ: World Scientific) pp 142-6
    • (1995) Advances in Dynamical Systems and Quantum Physics , pp. 142-146
    • Jona-Lasinio, G.1
  • 22
    • 0040634725 scopus 로고
    • On Schrödinger equations with concentrated nonlinearities
    • Jona-Lasinio G, Presilla C and Sjöstrand J 1995 On Schrödinger equations with concentrated nonlinearities Ann. Phys. 240 1-21
    • (1995) Ann. Phys. , vol.240 , Issue.1 , pp. 1-21
    • Jona-Lasinio, G.1    Presilla, C.2    Sjöstrand, J.3
  • 24
    • 0000818765 scopus 로고
    • Nonlinear Schrödinger equations
    • Kato T 1989 Nonlinear Schrödinger equations Schrödinger Operators (Lecture Notes in Physics vol 345) ed H Holden and A Jensen (Berlin: Springer) pp 218-63
    • (1989) Schrödinger Operators , pp. 218-263
    • Kato, T.1
  • 25
    • 77956935987 scopus 로고
    • Remarks on holomorphic families of Schrödinger and Dirac operators
    • Kato T 1984 Remarks on holomorphic families of Schrödinger and Dirac operators Differential Equations ed I W Knowles and R T Lewis (Amsterdam: Elsevier) pp 341-52
    • (1984) Differential Equations , pp. 341-352
    • Kato, T.1
  • 27
    • 0001608151 scopus 로고
    • Operator methods for inverse scattering on the real line
    • Melin A 1985 Operator methods for inverse scattering on the real line Commun. Partial Diff. Eqns 10 677-766
    • (1985) Commun. Partial Diff. Eqns , vol.10 , pp. 677-766
    • Melin, A.1
  • 29
    • 0000972578 scopus 로고
    • Non-linear feedback oscillations in resonant tunneling through double barriers
    • Presilla C, Jona-Lasinio G and Capasso F 1991 Non-linear feedback oscillations in resonant tunneling through double barriers Phys. Rev. B 43 5200-3
    • (1991) Phys. Rev. , vol.43 , Issue.6 , pp. 5200-5203
    • Presilla, C.1    Jona-Lasinio, G.2    Capasso, F.3
  • 30
    • 0030505856 scopus 로고    scopus 로고
    • Transport properties in resonant tunneling
    • Presilla C and Sjöstrand J 1996 Transport properties in resonant tunneling J. Math. Phys. 37 4816-44
    • (1996) J. Math. Phys. , vol.37 , Issue.10 , pp. 4816-4844
    • Presilla, C.1    Sjöstrand, J.2
  • 34
    • 84858942084 scopus 로고    scopus 로고
    • Tunneling destruction for a nonlinear Schrödinger equation
    • Sachetti A 2002 Tunneling destruction for a nonlinear Schrödinger equation Mathematical Results in Quantum Mechanics (Contemporary Mathematics vol 307) ed R Weder, P Exner and B Grébert (Providence, RI: American Mathematical Society) pp 275-9
    • (2002) Mathematical Results in Quantum Mechanics , pp. 275-279
    • Sachetti, A.1
  • 35
    • 84858932869 scopus 로고    scopus 로고
    • Nonlinear Time-dependent Schrödinger equation with double well potential
    • Sachetti A 2004 Nonlinear Time-dependent Schrödinger equation with double well potential Multiscale Methods in Quantum Mechanics ed P Blanchard and G Dell'Antonio (Basel: Birkhäuser)
    • (2004) Multiscale Methods in Quantum Mechanics
    • Sachetti, A.1
  • 36
    • 23744466181 scopus 로고    scopus 로고
    • Nonlinear double well Schrödinger equation in the semiclassical limit
    • Sachetti A 2005 Nonlinear double well Schrödinger equation in the semiclassical limit J. Stat. Phys. 119 1347-81
    • (2005) J. Stat. Phys. , vol.119 , Issue.5-6 , pp. 1347-1381
    • Sachetti, A.1
  • 37
    • 4444321157 scopus 로고    scopus 로고
    • Nonlinear time-dependent one-dimensional Schrödinger equation with a double well potential
    • Sachetti A 2004 Nonlinear time-dependent one-dimensional Schrödinger equation with a double well potential SIAM J. Math. Anal. 35 1160-76
    • (2004) SIAM J. Math. Anal. , vol.35 , Issue.5 , pp. 1160-1176
    • Sachetti, A.1
  • 42
    • 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 Commun. Math. Phys. 208 507-20
    • (1999) Commun. Math. Phys. , vol.208 , Issue.2 , pp. 507-520
    • Weder, R.1
  • 43
    • 0002283169 scopus 로고    scopus 로고
    • Estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
    • Weder R 2000 estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential J. Funct. Anal. 170 37-68
    • (2000) J. Funct. Anal. , vol.170 , Issue.1 , pp. 37-68
    • Weder, R.1
  • 44
    • 0034410054 scopus 로고    scopus 로고
    • Inverse scattering on the line for the nonlinear Klein-Gordon equation. Reconstruction of the potential and the nonlinearity
    • Weder R 2000 Inverse scattering on the line for the nonlinear Klein-Gordon equation. Reconstruction of the potential and the nonlinearity J. Math. Anal. Appl. 252 102-23
    • (2000) J. Math. Anal. Appl. , vol.252 , Issue.1 , pp. 102-123
    • Weder, R.1
  • 45
    • 0034349544 scopus 로고    scopus 로고
    • Center manifolds for nonintegrable nonlinear Schrödinger equations on the line
    • Weder R 2000 Center manifolds for nonintegrable nonlinear Schrödinger equations on the line Commun. Math. Phys. 215 343-56
    • (2000) Commun. Math. Phys. , vol.215 , Issue.2 , pp. 343-356
    • Weder, R.1
  • 46
    • 0034831729 scopus 로고    scopus 로고
    • Inverse scattering for the nonlinear Schrödinger equation. Reconstruction of the potential and the nonlinearity
    • Weder R 2001 Inverse scattering for the nonlinear Schrödinger equation. Reconstruction of the potential and the nonlinearity Math. Methods Appl. Sci. 24 245-54
    • (2001) Math. Methods Appl. Sci. , vol.24 , Issue.4 , pp. 245-254
    • Weder, R.1
  • 47
    • 23044531521 scopus 로고    scopus 로고
    • Inverse scattering for the nonlinear Schrödinger equation II. Reconstruction of the potential and the nonlinearity in the multidimensional case
    • Weder R 2001 Inverse scattering for the nonlinear Schrödinger equation II. Reconstruction of the potential and the nonlinearity in the multidimensional case Proc. Am. Math. Soc. 129 3637-45
    • (2001) Proc. Am. Math. Soc. , vol.129 , Issue.12 , pp. 3637-3645
    • Weder, R.1
  • 48
    • 0036747937 scopus 로고    scopus 로고
    • Multidimensional inverse scattering for the nonlinear Klein-Gordon equation with a potential
    • Weder R 2002 Multidimensional inverse scattering for the nonlinear Klein-Gordon equation with a potential J. Diff. Eqns 184 62-77
    • (2002) J. Diff. Eqns , vol.184 , Issue.1 , pp. 62-77
    • Weder, R.1
  • 49
    • 33748310391 scopus 로고    scopus 로고
    • The time dependent approach to inverse scattering
    • Weder R 2003 The time dependent approach to inverse scattering Advances in Differential Equations and Mathematical Physics (Contemporary Mathematics vol 327) ed J Karpeshina, G Stolz, R Weikard and Y Zeng (Providence, RI: American Mathematical Society) pp 359-77
    • (2003) Advances in Differential Equations and Mathematical Physics , pp. 359-377
    • Weder, R.1
  • 50
    • 20544443521 scopus 로고    scopus 로고
    • Scattering for the forced non-linear Schrödinger equation with a potential on the half-line
    • Weder R 2005 Scattering for the forced non-linear Schrödinger equation with a potential on the half-line Math. Methods Appl. Sci. 28 1219-36
    • (2005) Math. Methods Appl. Sci. , vol.28 , Issue.10 , pp. 1219-1236
    • Weder, R.1
  • 51
    • 20544469262 scopus 로고    scopus 로고
    • The forced non-linear Schrödinger equation with a potential on the half-line
    • Weder R 2005 The forced non-linear Schrödinger equation with a potential on the half-line Math. Methods Appl. Sci. 28 1237-55
    • (2005) Math. Methods Appl. Sci. , vol.28 , Issue.10 , pp. 1237-1255
    • Weder, R.1


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