Advertisement

Theoretical and Mathematical Physics

, Volume 102, Issue 2, pp 117–132 | Cite as

Scattering problem for the differential operator ∂ x y +1+a(x,y) y +a(x,y)

  • T. I. Garagash
  • A. K. Pogrebkov
Article

Abstract

The scattering problem for the two-dimensional Klein — Gordon differential operator with variable coefficients is studied in the framework of the resolvent approach. Jost solutions, retarded and advanced solutions, and spectral data are introduced, and their properties are described. The inverse scattering problem is formulated.

Keywords

Spectral Data Differential Operator Variable Coefficient Scatter Problem Inverse Scatter Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Boiti, J. Leon, L. Martini, and F. Pempinelli,Phys. Lett. A,132, 432 (1988).Google Scholar
  2. 2.
    M. Boiti, J. Leon, and F. Pempinelli,J. Math. Phys.,31, 2612 (1990).Google Scholar
  3. 3.
    A. S. Fokas and P. M. Santini,Phys. Rev. Lett.,63, 1329 (1989).Google Scholar
  4. 4.
    A. S. Fokas and P. M. Santini,Physica (Utrecht) D,44, 99 (1990).Google Scholar
  5. 5.
    M. Boiti, J. Leon, and F. Pempinelli,Inverse Problems,3, 37 (1987).Google Scholar
  6. 6.
    T. I. Garagash and A. K. Pogrebkov “Resolvent method for two-dimensional inverse problems” in:Nonlinear Evolution Equations and Dynamical Systems, Makhankov, I. Puzynin, and O. Pashaev, eds., World Scientific, Singapore (1992), p. 124.Google Scholar
  7. 7.
    P. G. Grinevich and S. V. Manakov,Funktsional. Analiz i Ego Prilozhen.,20, 14 (1986).Google Scholar
  8. 8.
    P. G. Grinevich and R. G. Novikov,Dokl. Akad. Nauk SSSR,286, 19 (1986).Google Scholar
  9. 9.
    A. P. Veselov and S. P. Novikov,Dokl. Akad. Nauk SSSR,279, 20 (1986).Google Scholar
  10. 10.
    P. G. Grinevich and S. P. Novikov,Funktsional. Analiz i Ego Prilozhen.,22, 23 (1988).Google Scholar
  11. 11.
    M. Boiti, J. Leon, and F. Pempinelli,Inverse Problems,3, 371 (1987).Google Scholar
  12. 12.
    M. Boiti, F. Pempinelli, A. K. Pogrebkov, and M. C. Polivanov, “Resolvent approach for the nonstationary Schrödinger equation (standard case of rapidly decreasing potential),” in:Proc. 7th Workshop on Nonlinear Evolution Equation and Dynamical Systems (NEEDS '91), World Scientific, Singapore (1992).Google Scholar
  13. 13.
    M. Boiti, F. Pempinelli, A. K. Pogrebkov, and M. C. Polivanov,Theor. Math. Phys.,93, 1200 (1992).Google Scholar
  14. 14.
    M. Boiti, F. Pempinelli, and A. Pogrebkov,Inverse Problems,10, 505 (1994).Google Scholar
  15. 15.
    M. Boiti, F. Pempinelli, and A. Pogrebkov,Teor. Mat. Fiz.,99, 185 (1994).Google Scholar
  16. 16.
    M. Boiti, F. Pempinelli and A. Pogrebkov, “Properties of solutions of the KPI equation,” to be published inJ. Math. Phys. (1994).Google Scholar
  17. 17.
    X. Zhou,SIAM J. Math. Anal. (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • T. I. Garagash
  • A. K. Pogrebkov

There are no affiliations available

Personalised recommendations