Wave scattering in one dimension with absorption

Journal of Mathematical Physics

Volumn 39, Issue 4, 1998, Pages 1957-1992

  Aktosun, Tuncay ^a   Klaus, Martin ^b   Van Der Mee, Cornelis ^c  

^a NORTH DAKOTA STATE UNIVERSITY   (United States)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^c UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032385701     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532271     Document Type: Article

References (31)

1. M. Jaulent and C. Jean, "The inverse s-wave scattering problem for a class of potentials depending on energy," Commun. Math. Phys. 28, 177-220 (1972).
2. M. Jaulent and C. Jean, "The inverse problem for the one-dimensional Schrödinger equation with an energy-dependent potential. I," Ann. Inst. Henri Poincaré, Sect. A 25, 105-118 (1976).
3. M. Jaulent and C. Jean, "The inverse problem for the one-dimensional Schrödinger equation with an energy-dependent potential. II," Ann. Inst. Henri Poincaré, Sect. A 25, 119-137 (1976).
4. M. Jaulent, "Inverse scattering problems in absorbing media," J. Math. Phys. 17, 1351-1360 (1976).
5. D. H. Sattinger and J. Szmigielski, "Energy dependent scattering theory," Differ. Integral Eqs. 8, 945-959 (1995).
6. D. J. Kaup, "A higher-order water-wave equation and the method for solving it," Prog. Theor. Phys. 54, 396-408 (1975).
7. M. Tsutsumi, "On the inverse scattering problem for the one-dimensional Schrödinger equation with an energy dependent potential," J. Math. Anal. Appl. 83, 316-350 (1981).
8. D. H. Sattinger and J. Szmigielski, "A Riemann-Hilbert problem for an energy dependent Schrödinger operator," Inverse Probl. 12, 1003-1025 (1996).
9. L. D. Faddeev, "Properties of the S-matrix of the one-dimensional Schrödinger equation," Am. Math. Soc. Trans. 2, 139-166 (1964) [Trudy Mat. Inst. Steklova 73, 314-336 (1964) (Russian)].
10. L. D. Faddeev, "Properties of the S-matrix of the one-dimensional Schrödinger equation," Am. Math. Soc. Trans. 2, 139-166 (1964) [Trudy Mat. Inst. Steklova 73, 314-336 (1964) (Russian)].
11. P. Deift and E. Trubowitz, "Inverse scattering on the line," Commun. Pure Appl. Math. 32, 121-251 (1979).
12. M. Klaus, "Low-energy behaviour of the scattering matrix for the Schrödinger equation on the line," Inverse Probl. 4, 505-512 (1988).
13. T. Aktosun, M. Klaus, and C. van der Mee, "Inverse wave scattering with discontinuous wave speed," J. Math. Phys. 36, 2880-2928 (1995).
14. V. N. Pivovarchik, "On the discrete spectrum of a boundary value problem," Sib. Math. J. 31, 853-856 (1990) [Sibirsk. Mat. Zh. 31, 182-186 (1990) (Russian)].
15. V. N. Pivovarchik, "On the discrete spectrum of a boundary value problem," Sib. Math. J. 31, 853-856 (1990) [Sibirsk. Mat. Zh. 31, 182-186 (1990) (Russian)].
16. V. N. Pivovarchik, "Eigenvalues of a certain quadratic pencil of operators," Funct. Anal. Appl. 23, 70-72 (1989) [Funkt. Anal. i ego Priloz. 23, 80-81 (1989) (Russian)].
17. V. N. Pivovarchik, "Eigenvalues of a certain quadratic pencil of operators," Funct. Anal. Appl. 23, 70-72 (1989) [Funkt. Anal. i ego Priloz. 23, 80-81 (1989) (Russian)].
18. V. N. Pivovarchik, "On the total algebraic multiplicity of the spectrum in the right-half plane for a quadratic operator pencil," St. Petersburg Math. J. 3, 447-454 (1992) [Algebra i Analiz 3, 223-230 (1991) (Russian)].
19. V. N. Pivovarchik, "On the total algebraic multiplicity of the spectrum in the right-half plane for a quadratic operator pencil," St. Petersburg Math. J. 3, 447-454 (1992) [Algebra i Analiz 3, 223-230 (1991) (Russian)].
20. V. N. Pivovarchik, "On positive spectra of one class of polynomial operator pencils," Integr. Eqs. Oper. Th. 19, 314-326 (1994).
21. R. P. Boas, Entire Functions (Academic, New York, 1954).
22. D. B. Hinton, M. Klaus, and J. K. Shaw, "Levinson's theorem and Titchmarsh-Weyl m(λ) theory for Dirac systems," Proc. R. Soc. Edinburgh Sect. A 109, 173-186 (1988).
23. I. C. Gohberg and E. I. Sigal, "An operator generalization of the logarithmic residue theorem and the theorem of Rouché," Math. USSR Sbornik 13, 603-625 (1971) [Mat. Sbornik 84, 607-629 (1971) (Russian)].
24. I. C. Gohberg and E. I. Sigal, "An operator generalization of the logarithmic residue theorem and the theorem of Rouché," Math. USSR Sbornik 13, 603-625 (1971) [Mat. Sbornik 84, 607-629 (1971) (Russian)].
25. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955).
26. N. Levinson, "On the uniqueness of the potential in a Schrödinger equation for a given asymptotic phase," Danske Vid. Selsk. Mat.-Fys. Medd. 25, 1-29 (1949).
27. J. Weidmann, Spectral Theory of Ordinary Differential Operators, Lecture Notes in Mathematics, 1258 (Springer, Berlin, 1987).
28. M. Reed and B. Simon, Methods of Modern Mathematical Physics. IV. Analysis of Operators (Academic, New York, 1978).
29. M. Reed and B. Simon, Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-adjointness (Academic, New York, 1975).
30. T. Kato, Perturbation Theory for Linear Operators, 2nd ed. (Springer, Berlin, 1976).
31. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).