메뉴 건너뛰기




Volumn 21, Issue 1, 2005, Pages 257-270

Formulae and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; IMAGE ANALYSIS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

EID: 13744250346     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/21/1/016     Document Type: Article
Times cited : (23)

References (34)
  • 1
    • 84972834699 scopus 로고
    • Stable determination of conductivity by boundary measurements
    • [A]
    • [A] Alessandrini G 1988 Stable determination of conductivity by boundary measurements Appl. Anal. 27 153-72
    • (1988) Appl. Anal. , vol.27 , pp. 153-172
    • Alessandrini, G.1
  • 2
    • 0007059921 scopus 로고
    • Multidimensional inverse scattering and nonlinear partial differential equations
    • [BC]
    • [BC] Beals R and Coifman R R 1985 Multidimensional inverse scattering and nonlinear partial differential equations Proc. Symp, Pure Math. 43 45-70
    • (1985) Proc. Symp, Pure Math. , vol.43 , pp. 45-70
    • Beals, R.1    Coifman, R.R.2
  • 3
    • 0345913370 scopus 로고    scopus 로고
    • Numerical realization of algorithm for exact solution of two-dimensional monochromatic inverse problem of acoustical scattering
    • [BBMRS] (New York: Kluwer)
    • [BBMRS] Bogatyrev A V, Burov V A, Morozov S A, Rumyantseva O D and Sukhov E G 2000 Numerical realization of algorithm for exact solution of two-dimensional monochromatic inverse problem of acoustical scattering Acoustical Imaging vol 25 (New York: Kluwer) pp 65-70
    • (2000) Acoustical Imaging , vol.25 , pp. 65-70
    • Bogatyrev, A.V.1    Burov, V.A.2    Morozov, S.A.3    Rumyantseva, O.D.4    Sukhov, E.G.5
  • 4
    • 0345913369 scopus 로고    scopus 로고
    • Reconstruction of fine-scale structure of acoustical scatterer on large-scale contrast background
    • [BMR] (New York: Kluwer)
    • [BMR] Burov V A, Morozov S A and Rumyantseva O D 2002 Reconstruction of fine-scale structure of acoustical scatterer on large-scale contrast background Acoustical Imaging vol 26 (New York: Kluwer) pp 231-8
    • (2002) Acoustical Imaging , vol.26 , pp. 231-238
    • Burov, V.A.1    Morozov, S.A.2    Rumyantseva, O.D.3
  • 5
    • 0000199057 scopus 로고    scopus 로고
    • Inverse scattering via Heisenberg's uncertainty principle
    • [Ch]
    • [Ch] Chen Yu 1997 Inverse scattering via Heisenberg's uncertainty principle Inverse Problems 13 253-82
    • (1997) Inverse Problems , vol.13 , pp. 253-282
    • Yu, C.1
  • 6
    • 10844223395 scopus 로고    scopus 로고
    • The inverse scattering problem in two dimensions at a fixed energy
    • [E]
    • [E] Eskin G 2001 The inverse scattering problem in two dimensions at a fixed energy Commun. Partial Diff. Eg. 26 1055-90
    • (2001) Commun. Partial Diff. Eg. , vol.26 , pp. 1055-1090
    • Eskin, G.1
  • 7
    • 0008131380 scopus 로고
    • Increasing solutions of the Shrödinger equation
    • [F1] (in Russian)
    • [F1] Faddeev L D 1965 Increasing solutions of the Shrödinger equation Dokl. Akad. Nauk SSSR 165 514-7 (in Russian) Faddeev L D 1966 Sov. Phys. Dokl. 10 1033-5 (Engl. Transl.)
    • (1965) Dokl. Akad. Nauk SSSR , vol.165 , pp. 514-517
    • Faddeev, L.D.1
  • 8
    • 0009639124 scopus 로고
    • Engl. Transl.
    • [F1] Faddeev L D 1965 Increasing solutions of the Shrödinger equation Dokl. Akad. Nauk SSSR 165 514-7 (in Russian) Faddeev L D 1966 Sov. Phys. Dokl. 10 1033-5 (Engl. Transl.)
    • (1966) Sov. Phys. Dokl. , vol.10 , pp. 1033-1035
    • Faddeev, L.D.1
  • 9
    • 0040394202 scopus 로고
    • Factorization of the S matrix for the multidimensional Shrödinger operator
    • [F2] (in Russian)
    • [F2] Faddeev L D 1966 Factorization of the S matrix for the multidimensional Shrödinger operator Dokl. Akad. Nauk SSSR 167 69-72 (in Russian) Faddeev L D 1966 Sov. Phys. Dokl. 11 209-11 (Engl. Transl.)
    • (1966) Dokl. Akad. Nauk SSSR , vol.167 , pp. 69-72
    • Faddeev, L.D.1
  • 10
    • 0000514698 scopus 로고
    • Engl. Transl.
    • [F2] Faddeev L D 1966 Factorization of the S matrix for the multidimensional Shrödinger operator Dokl. Akad. Nauk SSSR 167 69-72 (in Russian) Faddeev L D 1966 Sov. Phys. Dokl. 11 209-11 (Engl. Transl.)
    • (1966) Sov. Phys. Dokl. , vol.11 , pp. 209-211
    • Faddeev, L.D.1
  • 11
    • 0002477276 scopus 로고
    • Inverse problem of quantum scattering theory II
    • [F3] (in Russian)
    • [F3] Faddeev L D 1974 Inverse problem of quantum scattering theory II Itogi Nauki Tekhn. Sovrem. Prob. Mat. 3 93-180 (in Russian) Faddeev L D 1976 Inverse problem of quantum scattering theory II Sov. Math. 5 334-96 (Engl. Transl.)
    • (1974) Itogi Nauki Tekhn. Sovrem. Prob. Mat. , vol.3 , pp. 93-180
    • Faddeev, L.D.1
  • 12
    • 0001649173 scopus 로고
    • Inverse problem of quantum scattering theory II
    • Engl. Transl.
    • [F3] Faddeev L D 1974 Inverse problem of quantum scattering theory II Itogi Nauki Tekhn. Sovrem. Prob. Mat. 3 93-180 (in Russian) Faddeev L D 1976 Inverse problem of quantum scattering theory II Sov. Math. 5 334-96 (Engl. Transl.)
    • (1976) Sov. Math. , vol.5 , pp. 334-396
    • Faddeev, L.D.1
  • 13
    • 0041155301 scopus 로고
    • Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials
    • [GN]
    • [GN] Grinevich P G and Novikov R G 1995 Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials Commun. Math. Phys. 174 409-46
    • (1995) Commun. Math. Phys. , vol.174 , pp. 409-446
    • Grinevich, P.G.1    Novikov, R.G.2
  • 14
    • 0000451602 scopus 로고
    • The ∂̄-equation in the multidimensional inverse scattering problem
    • [HN] (in Russian)
    • [HN] Henkin G M and Novikov R G 1987 The ∂̄-equation in the multidimensional inverse scattering problem Usp. Mat. Nauk 42 (3) 93-152 (in Russian) Henkin G M and Novikov R G 1987 Russ. Math. Surv. 42 (3) 109-80 (Engl. Transl.)
    • (1987) Usp. Mat. Nauk , vol.42 , Issue.3 , pp. 93-152
    • Henkin, G.M.1    Novikov, R.G.2
  • 15
    • 0000451597 scopus 로고
    • Engl. Transl.
    • [HN] Henkin G M and Novikov R G 1987 The ∂̄-quation in the multidimensional inverse scattering problem Usp. Mat. Nauk 42 (3) 93-152 (in Russian) Henkin G M and Novikov R G 1987 Russ. Math. Surv. 42 (3) 109-80 (Engl. Transl.)
    • (1987) Russ. Math. Surv. , vol.42 , Issue.3 , pp. 109-180
    • Henkin, G.M.1    Novikov, R.G.2
  • 16
    • 0040174316 scopus 로고
    • The inverse scattering at fixed energies in two dimensions
    • [IS]
    • [IS] Isakov V and Sun Z 1995 The inverse scattering at fixed energies in two dimensions Indiana Univ. Math. J. 44 883-96
    • (1995) Indiana Univ. Math. J. , vol.44 , pp. 883-896
    • Isakov, V.1    Sun, Z.2
  • 17
    • 0343147099 scopus 로고
    • On the inverse scattering transform of the n-dimensional Schrödinger operator
    • [LN] ed M Ablovitz, B Fuchssteiner and M Kruskal (Singapore: World Scientific)
    • [LN] Lavine R B and Nachman AI 1987 On the inverse scattering transform of the n-dimensional Schrödinger operator Topics in Soliton Theory and Exactly Solvable Nonlinear Equations ed M Ablovitz, B Fuchssteiner and M Kruskal (Singapore: World Scientific) pp 33-44
    • (1987) Topics in Soliton Theory and Exactly Solvable Nonlinear Equations , pp. 33-44
    • Lavine, R.B.1    Nachman, A.I.2
  • 18
    • 0035473445 scopus 로고    scopus 로고
    • Exponential instability in an inverse problem for the Schrödinger equation
    • [M]
    • [M] Mandache N 2001 Exponential instability in an inverse problem for the Schrödinger equation Inverse Problems 17 1435-44
    • (2001) Inverse Problems , vol.17 , pp. 1435-1444
    • Mandache, N.1
  • 19
    • 0000426306 scopus 로고
    • Reconstructions from boundary measurements
    • [Nal]
    • [Nal] Nachman A I 1988 Reconstructions from boundary measurements Ann. Math. 128 531-76
    • (1988) Ann. Math. , vol.128 , pp. 531-576
    • Nachman, A.I.1
  • 20
    • 0030550779 scopus 로고
    • Global uniqueness for a two-dimensional inverse boundary value problem
    • [Na2]
    • [Na2] Nachman A I 1995 Global uniqueness for a two-dimensional inverse boundary value problem Ann. Math. 142 71-96
    • (1995) Ann. Math. , vol.142 , pp. 71-96
    • Nachman, A.I.1
  • 23
    • 0001875067 scopus 로고
    • Multidimensional inverse spectral problem for the equation -Δψ + (v(x) - Eu(x)) ψ = 0
    • [Nol] (in Russian)
    • [Nol] Novikov R G 1988 Multidimensional inverse spectral problem for the equation -Δψ + (v(x) - Eu(x)) ψ = 0 Funkt. Anal. Ego Pril. 22 (4) 11-22 (in Russian) Novikov R G 1988 Funct. Anal. Appl. 22 263-72 (Engl. Transl.)
    • (1988) Funkt. Anal. Ego Pril. , vol.22 , Issue.4 , pp. 11-22
    • Novikov, R.G.1
  • 24
    • 34249973239 scopus 로고
    • Engl. Transl.
    • [Nol] Novikov R G 1988 Multidimensional inverse spectral problem for the equation -Δψ + (v(x) - Eu(x)) ψ = 0 Funkt. Anal. Ego Pril. 22 (4) 11-22 (in Russian) Novikov R G 1988 Funct. Anal. Appl. 22 263-72 (Engl. Transl.)
    • (1988) Funct. Anal. Appl. , vol.22 , pp. 263-272
    • Novikov, R.G.1
  • 25
    • 0010533416 scopus 로고
    • The inverse scattering problem on a fixed energy level for the two-dimensional Schrödinger operator
    • [No2]
    • [No2] Novikov R G 1992 The inverse scattering problem on a fixed energy level for the two-dimensional Schrödinger operator J. Funct. Anal. 103 409-63
    • (1992) J. Funct. Anal. , vol.103 , pp. 409-463
    • Novikov, R.G.1
  • 26
    • 21344497080 scopus 로고
    • The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential
    • [No3]
    • [No3] Novikov R G 1994 The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential Commun. Math. Phys. 161 569-95
    • (1994) Commun. Math. Phys. , vol.161 , pp. 569-595
    • Novikov, R.G.1
  • 27
    • 0039470247 scopus 로고    scopus 로고
    • ∂̄-method with nonzero background potential. Application to inverse scattering for the two-dimensional acoustic equation
    • [No4]
    • [No4] Novikov R G 1996 ∂̄-method with nonzero background potential. Application to inverse scattering for the two-dimensional acoustic equation Commun. Partial Diff. Eq. 21 597-618
    • (1996) Commun. Partial Diff. Eq. , vol.21 , pp. 597-618
    • Novikov, R.G.1
  • 28
    • 13744251603 scopus 로고    scopus 로고
    • Approximate inverse quantum scattering at fixed energy in dimension
    • [No5]
    • [No5] Novikov R G 1999 Approximate inverse quantum scattering at fixed energy in dimension 2 Proc. Steklov Inst. Math. 225 285-302
    • (1999) 2 Proc. Steklov Inst. Math. , vol.225 , pp. 285-302
    • Novikov, R.G.1
  • 29
    • 13744256383 scopus 로고    scopus 로고
    • Scattering for the Schrödinger equation in multidimension non-linear ∂̄-equation, characterization of scattering data and related results
    • [No6] ed E R Pike and P Sabatier (New York: Academic) chapter 6.2.4
    • [No6] Novikov R G 2002 Scattering for the Schrödinger equation in multidimension non-linear ∂̄-equation, characterization of scattering data and related results Scattering ed E R Pike and P Sabatier (New York: Academic) chapter 6.2.4
    • (2002) Scattering
    • Novikov, R.G.1
  • 30
    • 0001658677 scopus 로고
    • Stability of the inverse problem in potential scattering at fixed energy
    • [St1]
    • [St1] Stefanov P 1990 Stability of the inverse problem in potential scattering at fixed energy Ann. Inst. Fourier Grenoble 40 867-84
    • (1990) Ann. Inst. Fourier Grenoble , vol.40 , pp. 867-884
    • Stefanov, P.1
  • 31
    • 0012095350 scopus 로고
    • A uniqueness result for the inverse back-scattering problem
    • [St2]
    • [St2] Stefanov P 1990 A uniqueness result for the inverse back-scattering problem Inverse Problems 6 1055-64
    • (1990) Inverse Problems , vol.6 , pp. 1055-1064
    • Stefanov, P.1
  • 32
    • 0001110912 scopus 로고
    • A global uniqueness theorem for an inverse boundary value problem
    • [SU]
    • [SU] Sylvester J and Uhlmann G 1987 A global uniqueness theorem for an inverse boundary value problem Ann. Math. 125 153-69
    • (1987) Ann. Math. , vol.125 , pp. 153-169
    • Sylvester, J.1    Uhlmann, G.2
  • 33
    • 0000452814 scopus 로고
    • Global uniqueness at fixed energy in multidimensional inverse scattering theory
    • [We1]
    • [We1] Weder R 1991 Global uniqueness at fixed energy in multidimensional inverse scattering theory Inverse Problems 7 927-38
    • (1991) Inverse Problems , vol.7 , pp. 927-938
    • Weder, R.1
  • 34
    • 84988158548 scopus 로고
    • Generalized limiting absorption method and multidimensional inverse scattering theory
    • [We2]
    • [We2] Weder R 1991 Generalized limiting absorption method and multidimensional inverse scattering theory Math. Methods Appl. Sci. 14 509-24
    • (1991) Math. Methods Appl. Sci. , vol.14 , pp. 509-524
    • Weder, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.