Geodesic
Asymptotic Solutions of Two-Dimensional Hartree-Type Equations Localized in the Neighborhood of Line Segments
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 3, pp. 389-406

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

We consider the eigenvalue problem for the two-dimensional Schrödinger equation containing an integral Hartree-type nonlinearity with an interaction potential having a logarithmic singularity. Global asymptotic solutions localized in the neighborhood of a line segment in the plane are constructed using the matching method for asymptotic expansions. The Bogoliubov and Airy polarons are used as model functions in these solutions. An analogue of the Bohr–Sommerfeld quantization rule is established to find the related series of eigenvalues. 
@article{TMF_2002_131_3_a2,
     author = {A. V. Pereskokov},
     title = {Asymptotic {Solutions} of {Two-Dimensional} {Hartree-Type} {Equations} {Localized} in the {Neighborhood} of {Line} {Segments}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {389--406},
     publisher = {mathdoc},
     volume = {131},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_3_a2/}
}
TY  - JOUR
AU  - A. V. Pereskokov
TI  - Asymptotic Solutions of Two-Dimensional Hartree-Type Equations Localized in the Neighborhood of Line Segments
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 389
EP  - 406
VL  - 131
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_131_3_a2/
LA  - ru
ID  - TMF_2002_131_3_a2
ER  - 
%0 Journal Article
%A A. V. Pereskokov
%T Asymptotic Solutions of Two-Dimensional Hartree-Type Equations Localized in the Neighborhood of Line Segments
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 389-406
%V 131
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2002_131_3_a2/
%G ru
%F TMF_2002_131_3_a2
A. V. Pereskokov. Asymptotic Solutions of Two-Dimensional Hartree-Type Equations Localized in the Neighborhood of Line Segments. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 3, pp. 389-406. http://geodesic.mathdoc.fr/item/TMF_2002_131_3_a2/