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Abstracts
In this work, we present some results showing
the controllability of the linear Schrödinger equation with
complex potentials. Firstly we investigate the existence
and uniqueness theorem for solution of the considered
problem. Then we find the gradient of the cost functional
with the help of HamiltonPontryagin functions. Finally
we state a necessary condition in the form of variational
inequality for the optimal solution using this gradient.
the controllability of the linear Schrödinger equation with
complex potentials. Firstly we investigate the existence
and uniqueness theorem for solution of the considered
problem. Then we find the gradient of the cost functional
with the help of HamiltonPontryagin functions. Finally
we state a necessary condition in the form of variational
inequality for the optimal solution using this gradient.
Journal
Year
Volume
Issue
Physical description
Dates
accepted
26  11  2015
received
28  9  2015
online
31  12  2015
Contributors
author

Department of Mathematics,
Ağrı İbrahim Çeçen Universty,Faculty of Science and
Art,Ağrı,Turkey
author

Department of Mathematics, Ataturk University,
Faculty of Science, Erzurum, Turkey
author

Department of Mathematics, Kafkas University,
Faculty of Science and Art, Kars, Turkey
References
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 [3] A. D. Iskenderov, Definition of a potential in Schrödingers’ nonstationaryequation. In: Problemi moton. Modelşrovania andopmolno go upravleva, Bakü, 2001, pp.636 (in Russian)
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 [9] N.Y. Aksoy, B. Yildiz, H. Yetiskin, Variational problem with complexcoeflcient of a nonlinear Schrödinger equation Proceedingsof the Indian Academy of Sciences:Mathematical Sciences,2012, 122 (3), pp. 469484
 [10] Y. Koçak, E. Çelik, Optimal control problem for stationary quasiopticequations, Boundary Value Problems 2012, 2012:151
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 [12] G.Ya. Yagubov, N.S. Ibrahimov, Optimal control problem fornonstationary quasi optic equation, Problems of mathematicalmodeling and optimal control, Baku, 2001, pp. 4957 (in Russian).
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 [14] G.Ya. Yagubov, M.A. Musayeva, On the identification problemfor nonlinear Schrödinger equation, Differentsial’niye uravneniya3(12) (1997) 1691–1698 (in Russian)
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 [16] M. Koksal, M.E. Koksal, Commutativity of Cascade ConnectedDiscrete Time Linear TimeVarying Systems, Transactions of theInstitute of Measurement and Control, 2015, 37 (5) 615622
 [17] M.A. Vorontsov, V. I. Shmalgauzen, Principles of adaptive optics.Moscow, Izdatel’stvo Nauka, 1985, 336 p. (in Russian)
 [18] K. Yosida, Functional analysis. Springer, 1980
 [19] O.A. Ladyzhanskaya, V.A. Sollonnikov, N.M. Uraltseva, Linearand Quasi Linear Equations of Parabolic Type, Translation ofMathematical Monographs. AMS, Rhode Island, 1968
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Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjddoi10_1515_phys20150051