Advertisement

Letters in Mathematical Physics

, Volume 31, Issue 3, pp 179–193 | Cite as

Characterization of the Weyl solutions

  • Vladimir A. Marchenko
Article

Abstract

For the Weyl solutionsθ(z, x) of the Schrödinger and Dirac equations, asymptotics for |z| → ∞ are obtained. This gives a possibility of selecting Weyl solutions by their behaviour when |z| → ∞. Some applications are given.

Mathematics Subject Classifications (1991)

34B20 34L40 35J20 35Q53 35Q55 81Q05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Marchenko, V. A., The Cauchy problem for the KdV equation with non-decreasing initial data, in V. E. Zaharov (ed.),What is Integrability?, Springer-Verlag, New York, 1990, pp. 273–318.Google Scholar
  2. 2.
    Levitan, B. M. and Sargsyan, I. S.,Introduction to the Spectral Theory, Nauka, Moscow, 1970, p. 671 (in Russian).Google Scholar
  3. 3.
    Martinov, V. V., Conditions of discreteness and continuity of spectrum in the case of a self-adjoint system of first-order differential equations,Dokl. Akad. Nauk SSSR 165, 996–999 (1965).Google Scholar
  4. 4.
    Marchenko, V. A., Asymptotics of the Weyl solutions of the Sturm-Liouville equations with respect to the spectral parameter,Proc. LOMI Seminars, v. 170, Nauka, Leningrad, pp. 184–206.Google Scholar
  5. 5.
    Misyura, T. V., Asymptotic formula for the Weyl solutions of the Dirac equations,Dokl. Akad. Nauk Ukrain. SSR 5, 26–28 (1991).Google Scholar
  6. 6.
    Marchenko, V. A.,The Sturm-Liouville Operators and Applications, Birkhäuser Verlag, Basel, 1986, p. 367.Google Scholar
  7. 7.
    Glazman, I. M.,Direct Method of Qualitative Analysis of Singular Differential Operators, Fizmatgiz, Moscow, 1963, p. 340 (in Russian).Google Scholar
  8. 8.
    Marchenko, V. A., Characterization of the Weyl solutions, Preprint BIBOS No 578/93, Universität Bielefeld.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Vladimir A. Marchenko
    • 1
  1. 1.MDILTPKharkovUkraine

Personalised recommendations