@article{JMAG_2018_14_2_a6,
author = {G. Yagub and N. S. Ibrahimov and M. Zengin},
title = {The solvability of the initial-boundary value problems for a nonlinear {Schr\"odinger} equation with a special gradient term},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {214--232},
year = {2018},
volume = {14},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_2018_14_2_a6/}
}
TY - JOUR AU - G. Yagub AU - N. S. Ibrahimov AU - M. Zengin TI - The solvability of the initial-boundary value problems for a nonlinear Schrödinger equation with a special gradient term JO - Žurnal matematičeskoj fiziki, analiza, geometrii PY - 2018 SP - 214 EP - 232 VL - 14 IS - 2 UR - http://geodesic.mathdoc.fr/item/JMAG_2018_14_2_a6/ LA - en ID - JMAG_2018_14_2_a6 ER -
%0 Journal Article %A G. Yagub %A N. S. Ibrahimov %A M. Zengin %T The solvability of the initial-boundary value problems for a nonlinear Schrödinger equation with a special gradient term %J Žurnal matematičeskoj fiziki, analiza, geometrii %D 2018 %P 214-232 %V 14 %N 2 %U http://geodesic.mathdoc.fr/item/JMAG_2018_14_2_a6/ %G en %F JMAG_2018_14_2_a6
G. Yagub; N. S. Ibrahimov; M. Zengin. The solvability of the initial-boundary value problems for a nonlinear Schrödinger equation with a special gradient term. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 2, pp. 214-232. http://geodesic.mathdoc.fr/item/JMAG_2018_14_2_a6/
[1] G. D. Akbaba, The Optimal Control Problem with the Lions Functional for the Schrödinger Equation Including Virtual Coefficient Gradient, Master's thesis, Kars, Turkey, 2011 (Turkish)
[2] L. Baudouin, O. Kavian, J. P. Puel, “Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control”, J. Differential Equations, 216 (2005), 188–222 | DOI | MR | Zbl
[3] A. G. Butkovskiy, Y. I. Samojlenko, Control of Quantum-Mechanical Processes and Systems, Mathematics and its Applications (Soviet Series), 56, Kluwer Academic Publishers Group, Dordrecht, 1990 | DOI | MR | Zbl
[4] N. S. Ibragimov, “The solvability of the initial-boundary value problems for the nonlinear stationary equation of quasi-optics with purely imaginary coefficient in the nonlinear part”, News of Baku State University, Ser. Physics and Math. Sciences, 2010, No. 3, 72–84
[5] A. D. Iskenderov, G. Y. Yagubov, “A variational method for solving an inverse problem of determining the quantum mechanical potential”, Dokl. Akad. Nauk SSSR, 303 (1988), 1044–1048 (Russian); Engl. transl.: Soviet Math. Dokl. | MR
[6] Automat. Remote Control, 50:12-1 (1989), 1631–1641 | MR | Zbl
[7] A. Iskenderov, G. Yagubov, “Optimal control of the unbounded potential in the multidimensional nonlinear nonstationary Schrödinger equation”, Bulletin of Lankaran State University, Ser. Natural Sciences, 2007, 3–56
[8] A. D. Iskenderov, G. Y. Yagubov, M. A. Musayeva, Identification of the Quantum Potentials, Chashyoglu, Baku, 2012 (Azerbaijani)
[9] M. Jahanshahi, S. Ashrafi, N. Aliev, “Boundary layer problem for the system of the first order ordinary differential equations with constant coefficients by general nonlocal boundary conditions”, Adv. Math. Models Appl., 2 (2017), 107–116
[10] O. A. Ladyzhenskaya, Boundary-Value Problems of Mathematical Physics, Nauka, M., 1973 (Russian) | MR
[11] Translations of Mathematical Monographs, 23, Amer. Math. Soc., Providence, R.I., 1968 | DOI | MR | Zbl
[12] J.-L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, v. I, Die Grundlehren der mathematischen Wissenschaften, 181, Springer-Verlag, New York–Heidelberg, 1972 | MR | Zbl
[13] L. S. Pontryagin, Ordinary Differential Equations, Nauka, M., 1982 | MR | Zbl
[14] F. P. Vasilyev, Numerical Methods for Solving of the Extremal Problems, Nauka, M., 1980 | MR
[15] M. A. Vorontsov, V. I. Schmalhausen, The Principles of Adaptive Optics, Nauka, M., 1985 (Russian) | MR
[16] G. Y. Yagubov, M. A. Musayeva, “On an identification problem for nonlinear Schrödinger equation”, Differ. Uravn., 33 (1997), 1691–1698 | MR | Zbl
[17] G. Yagubov, F. Toyğolu, M. Subaşı, “An optimal control problem for two-dimensional Schrödinger equation”, Appl. Math. Comput., 218 (2012), 6177–6187 | MR | Zbl
[18] K. Yajima, G. Zhang, “Smoothing property for Schrödinger equations with potential superquadratic at infinity”, Comm. Math. Phys., 221 (2001), 573–590 | DOI | MR | Zbl
[19] V. M. Zhuravlev, Nonlinear Waves in Multicomponent Systems Dispersion and Diffusion, Ulyanovsk State University, Ulyanovsk, 2001 (Russian)