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On the inverse problem of the Scattering Theory for a class of systems of dirac equations with discontiunous coefficient

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2008

Key Words:

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AMS Codes:

Abstract (2. Language): 
In this paper it is devoted to study the inverse scattering problem for a singular boundary value problem of generalized form of system Dirac type. The new representation for the solutions of the differential equations system is considered, the scattering function is defined and its properties are given. The main equation is obtained for the solution of the inverse problem and it is shown the uniqueness of the solution of the inverse problem of scattering theory on the half line [0,1).
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  • 3
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  • Turkish

REFERENCES

References: 

[1] T. Aktosun, Construction of the half-line potential from the Jost function. Inverse Problems 20, 3:
859-876 (2004).
[2] B. M. Levitan, The inverse scattering problem of quantum theory. Math. Notes 17:611-624 (1975).
[3] B. M. Levitan, Inverse Sturm-Liouville Problems. Utrecht:VNU Science Press BV, 1987.
[4] V. A. Marchenko, Sturm-Liouville Operators and Their Applications. Basel: Birkhauser, 1986.
[5] M. G. Gasymov, The inverse scattering problem for a system of Dirac equations of order 2n. Trans.
Moscow Math. Soc., 19:41–120 (1968) (Trudy Moskov. Mat. Obshch., 19:41-42 (1968)).
[6] M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform. SIAM Stud. Appl. Math. 4,
Society for Industrial and Applied Mathematics, Philadelphia, 1981.
[7] M. G. Gasymov, B. M. Levitan, Determination of Dirac system from scattering phase. DAN SSSR
167, 6:1219-1222 (1966) (in Russian).
[8] M. G. Gasymov, The direct and inverse problem of spectral analysis for a class of equations with a
discontinuous coefficient, in Non- classical methods in geophysics, Novosibirsk Nauka, 37- 44, 1977
(in Russian)
[9] I. M. Guseinov, On the representation of Jost solutions for Dirac’s equation system with discontinuous
coefficients. Transactions of AS Azerbaijan, 5:41-45 (1999).
[10] I. M. Guseinov, The inverse problem of scattering theory for Dirac system of equations with
discontinuous coefficients. Dokl. Akad. Nauk Azerb., 55, 1-2: 13-18 (1999).
[11] I. M. Guseinov, R. T. Pashaev, On an inverse problem for a second -order differential equation.
Uspekhi Math Nauk 57:147-148 (2002).
[12] Kh. R. Mamedov, Uniqueness of the solution of the inverse problem of scattering theory for
Sturm-Liouville operator with discontinuous coefficient. Proceedings of IMM of Nas Azerbaijan
24:163-172 (2006).
[13] B. M. Levitan, I. S. Sargsjan, Sturm-Liouville and Dirac Operators. Kluwer Academic Publishers,
Dordrecht, Boston London, 1991.
[14] Kh. R. Mamedov, On the inverse problem of scattering theory for a Dirac equations system, in
Abstracts Book of International Scientific ConferenceMathematical Analysis, Differential Equations
and their Applications, September 18-23, 2006, Uzhgorod, Ukraine.

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