Geodesic
Scattering problem for one non-self-adjoint Sturm--Liouville operator
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 120-126.

Voir la notice de l'article provenant de la source Math-Net.Ru

The scattering problem is considered for a class of second-order differential equations on a semi-infinite interval with a nonlinear spectral parameter in the boundary condition. The scattering data of the problem are determined and the fundamental equation of the inverse scattering problem is obtained.
Keywords: normalization polynomial, scattering function, scattering data, fundamental equation. 
@article{INTO_2023_226_a11,
     author = {R. G. Farzullazadeh and Kh. R. Mamedov},
     title = {Scattering problem for one non-self-adjoint {Sturm--Liouville} operator},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {120--126},
     publisher = {mathdoc},
     volume = {226},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_226_a11/}
}
TY  - JOUR
AU  - R. G. Farzullazadeh
AU  - Kh. R. Mamedov
TI  - Scattering problem for one non-self-adjoint Sturm--Liouville operator
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 120
EP  - 126
VL  - 226
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_226_a11/
LA  - ru
ID  - INTO_2023_226_a11
ER  - 
%0 Journal Article
%A R. G. Farzullazadeh
%A Kh. R. Mamedov
%T Scattering problem for one non-self-adjoint Sturm--Liouville operator
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 120-126
%V 226
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_226_a11/
%G ru
%F INTO_2023_226_a11
R. G. Farzullazadeh; Kh. R. Mamedov. Scattering problem for one non-self-adjoint Sturm--Liouville operator. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 120-126. http://geodesic.mathdoc.fr/item/INTO_2023_226_a11/

[1] Levitan B. M., “K resheniyu obratnoi zadachi kvantovoi teorii rasseyaniya”, Mat. zametki., 17:4 (1975), 611–624 | MR | Zbl

[2] Levitan B. M., Obratnye zadachi Shturma—Liuvillya, Nauka, M., 1984 | MR

[3] Lyantse V. E., “Analog obratnoi zadachi teorii rasseyaniya dlya nesamosopryazhennogo operatora”, Mat. sb., 72:4 (1967), 537–557 | Zbl

[4] Mamedov Kh. R., “Edinstvennost resheniya obratnoi zadachi teorii rasseyaniya dlya operatora Shturma—Liuvillya so spektralnym parametrom v granichnom uslovii”, Mat. zametki., 74:1 (2003), 142–146 | DOI | MR | Zbl

[5] Mamedov Kh. R., Demirbilek U., “Ob obratnoi zadache rasseyaniya dlya odnogo klassa operatorov Shturma—Liuvillya”, Itogi nauki tekhn. Ser. Sovr. mat. prilozh. Temat. obz., 200 (2021), 81–86 | DOI

[6] Marchenko V. A., Operatory Shturma—Liuvilya i ikh prilozheniya, Naukova dumka, Kiev, 1977 | MR

[7] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969

[8] Yurko V. A., “Obratnaya zadacha dlya puchkov differentsialnykh operatorov”, Mat. sb., 191:10 (2000), 137–160 | DOI | Zbl

[9] Cohen D. S., “An integral transform associated with boundary conditions containing an eigenvalue parameter”, SIAM J. Appl. Math., 14 (1966), 1164–1175 | DOI | MR | Zbl

[10] Col A., Mamedov Kh. R., “On an inverse scattering problem for a class of Dirac operators with spectral parameter in the boundary condition”, J. Math. Anal. Appl., 393 (2012), 470–478 | DOI | MR | Zbl

[11] Mamedov Kh. R., “On the inverse problem for Sturm-Liouville operator with a nonlinear spectral parameter in the boundary condition”, J. Korean Math. Soc., 46 (2009), 1243–1254 | DOI | MR | Zbl

[12] Mamedov Kh. R., Kosar P. A., “Inverse scattering problem for Sturm–Liouville operator with a nonlinear dependence on the spectral parameter in the boundary condition”, Math. Meth. Appl. Sci., 34:2, 231–241 | DOI | MR | Zbl

[13] Mamedov Kh. R., Menken H., “On the inverse problem of scattering theory for a differential operator of the second order”, Funct. Anal. Appl., 197 (2004), 185–194 | MR | Zbl

[14] McLaughlin J. R., Polyakov P. L., “On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues”, J. Differ. Equations., 107 (1994), 351–382 | DOI | MR | Zbl

[15] Megrabov A. G., Forward and Inverse Problems for Hyperbolic, Elliptic and Mixed Type Equations, VSP, Boston–Utrecht, 2003 | MR | Zbl

[16] Yang Q., Wang W., “Asymptotic behavior of a discontinuous differential operator with transmission conditions”, Math. Appl., 24 (2011), 15–24 | MR