Buradasınız

Anasayfa » Content

Basamak türünden potansiyele sahip Sturm-Liouville denkleminin ikinci dereceden demetinin çözümleri üzerine

On the solutions of the quadratic pencil of the Sturm-Liouville equation with steplike potential

Journal Name:

  • Cumhuriyet Üniversitesi Fen Fakültesi Fen Bilimleri Dergisi

Publication Year:

  • 2008

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
The Jost solutions of the quadratic pencil of the Sturm-Liouville equation with steplike potential are investigated on the real line. The Jost solutions are defined when the potential is asymptotic to different constants as x —» +oo,-oo. The integral representations are obtained for the Jost solutions and some spectral properties are investigated.
Bookmark/Search this post with
Abstract (Original Language): 
Bu çalışmada reel eksende basamak türünden potansiyele sahip Sturm-Liouville denkleminin ikinci dereceden demetinin Jost çözümleri incelenmektedir. Potansiyelin x —> +oo,—oo. iken farklı sabitlere yaklaşması durumu için Jost çözümleri belirlenmektedir. Jost çözümleri için integral gösterilimler elde edilmekte ve bazı spektral özellikler incelenmektedir.
FULL TEXT (PDF): 
PDF icon arastrmx_32114_29_pp_47-56.pdf
  • 1
47-56
  • Turkish

REFERENCES

References: 

[1] V.S. Buslaev and V.N. Fomin, An inverse scattering problem for the one dimensional Schrödinger equation on the entire axis (in Russian), VestnikLeningrad Univ., 17(1962), 56-64.
[2] E.J. Hruslov, Asymptotics of the solution of the Cauchy problem for the Korteweg-de Vries equation with initial data of step type, Math USSR-Sb., 28(9)(1976), 229¬248.
55
[3] M. Jaulent and C. Jean, The inverse problem for the one dimensional Schrödinger
equation with an energy dependent potential, I, II. Ann.Inst.Henri Poincare,
25(1976), 105-118, 119-137. [4] G.Sh. Guseinov and F.G. Maksudov, On solution of the inverse scattering problem
for a quadratic pencil of one-dimensional Schrödinger operators on the whole axis,
Dokl. Akad. NaukSSSR, 289(1)(1986), 42-46. [5] A. Cohen, A counterexample in the inverse scattering theory for steplike potentials,
Comm. Partial Differential Equations, 7(1982), 883-904. [6] A. Cohen and T. Kappeler, Scattering and Inverse Scattering for Steplike Potentials
in the Schrödinger equation, Indiana University Matematics Journal, 34(1)(1985),
127-180.
[7] İ.A. Anders and V.P. Kotlyarov, Characterization of the scattering data of the Schrödinger and Dirac operators, Theoretical and Mathematical Physics, 88(1)(1991), 725-734,
[8] V. A. Ditkin and A.P. Prudnikov, Integral transforms and operational calculus,
Pergamon Pres, New York, 1965.

Thank you for copying data from http://www.arastirmax.com