Inverse Scattering for a Small Nonselfadjoint Perturbation of the Wave Equation

  • Kiyoshi Mochizuki
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 10)


In this paper we consider the wave equation □u + b(x)u t = 0 in R n , n ≥ 3, with b(x) which is small and decays exponentially as |x| → ∞. We show that the scattering operator exists for each given b(x) and inversely the scattering amplitude at fixed nonzero energy determines the coefficient b(x).


Wave Equation Reconstruction Procedure Scattering Amplitude Inverse Scattering Selfadjoint Operator 
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  1. [1]
    Eskin, G., Ralston, J.: Inverse scattering problem fot the Schrödinger equation with magnetic potential with a fixed energy. Comm. Math. Phys. 173 (1995), 199–224.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Faddeev, L.D.: Uniqueness of the inverse scattering problem. Vestnik Leningrad Univ. 11 (1956), 126–130.MathSciNetGoogle Scholar
  3. [3]
    Faddeev, L.D.: Inverse problem of quantum scattering theory. J. Sov. Math. 5 (1976), 334–396.zbMATHCrossRefGoogle Scholar
  4. [4]
    Isozaki, H.: Inverse scattering theory for Dirac operators. Ann. Inst. H. Poincaré Physique Théorique 66 (1997), 237–270.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Isozaki, H.: Inverse problem theory for wave equations in stratified media. J. Differential Equations 138 (1997), 19–54.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    Kato, T.: Wave operators and similarity for some non-selfadjoint operators. Math. Ann. 162 (1966), 255–279.CrossRefGoogle Scholar
  7. [7]
    Mochizuki, K.: Eigenfunction expansions associated with the Schrödinger operator with a complex potential and the scattering inverse problem. Proc. Japan Acad. 43 (1967), 638–643.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Mochizuki, K.: Spectral and scattering theory for second order elliptic differential operators in an exterior domain. Lecture Notes Univ. Utah, Winter and Spring 1972.Google Scholar
  9. [9]
    Mochizuki, K.: Scattering theory for wave equations with dissipative term. Publ. Res. Inst. Math. Sci. 12 (1976), 383–390.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    Mochizuki, K.: Scattering theory for wave equations. Kinokuniya, 1983 (in Japanese).Google Scholar
  11. [11]
    Weder, R.: Generalized limiting absorption method and multidimensional inverse scattering theory. Math. Meth. in Appl. Sci. 14 (1991), 509–524.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Kiyoshi Mochizuki
    • 1
  1. 1.Department of MathematicTokyo Metropolitan UniversityHachioji, TokyoJapan

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