Geodesic
Construction of regularized asymptotics for the solution of a singularly perturbed mixed problem on the half-axis for the inhomogeneous Schr\"odinger-type equation with the potential $V(x)=x$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 27-43

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

In this paper, we propose a method for constructing an asymptotic solution to a singularly perturbed mixed problem on the half-axis for a nonstationary inhomogeneous Schrödinger-type equation in the coordinate representation in the case of violation of the stability conditions for the spectrum of the limit operator. The chosen profile of the potential energy leads to a spectral singularity of the limit operator, which, within the framework of S. A. Lomov's regularization method, is usually called a strong turning point.
Keywords: singularly perturbed problem, asymptotic solution, turning point, regularization method, semiclassical approximation 
@article{INTO_2024_231_a2,
     author = {A. G. Eliseev and P. V. Kirichenko},
     title = {Construction of regularized asymptotics for the solution of a singularly perturbed mixed problem on the half-axis for the inhomogeneous {Schr\"odinger-type} equation with the potential $V(x)=x$},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {27--43},
     publisher = {mathdoc},
     volume = {231},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2024_231_a2/}
}
TY  - JOUR
AU  - A. G. Eliseev
AU  - P. V. Kirichenko
TI  - Construction of regularized asymptotics for the solution of a singularly perturbed mixed problem on the half-axis for the inhomogeneous Schr\"odinger-type equation with the potential $V(x)=x$
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2024
SP  - 27
EP  - 43
VL  - 231
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2024_231_a2/
LA  - ru
ID  - INTO_2024_231_a2
ER  - 
%0 Journal Article
%A A. G. Eliseev
%A P. V. Kirichenko
%T Construction of regularized asymptotics for the solution of a singularly perturbed mixed problem on the half-axis for the inhomogeneous Schr\"odinger-type equation with the potential $V(x)=x$
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2024
%P 27-43
%V 231
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2024_231_a2/
%G ru
%F INTO_2024_231_a2
A. G. Eliseev; P. V. Kirichenko. Construction of regularized asymptotics for the solution of a singularly perturbed mixed problem on the half-axis for the inhomogeneous Schr\"odinger-type equation with the potential $V(x)=x$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 27-43. http://geodesic.mathdoc.fr/item/INTO_2024_231_a2/