Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 14, Tome 140 (1984), pp. 6-17
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V. M. Babich; V. P. Smyshlyaev. Scattering problem for the Schrödinger equation in the case of a potential linear in time and coordinate. I. Asymptotics in the shadow zone. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 14, Tome 140 (1984), pp. 6-17. http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a0/
@article{ZNSL_1984_140_a0,
author = {V. M. Babich and V. P. Smyshlyaev},
title = {Scattering problem for the {Schr\"odinger} equation in the case of a~potential linear in time and {coordinate.~I.} {Asymptotics} in the shadow zone},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {6--17},
year = {1984},
volume = {140},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a0/}
}
TY - JOUR
AU - V. M. Babich
AU - V. P. Smyshlyaev
TI - Scattering problem for the Schrödinger equation in the case of a potential linear in time and coordinate. I. Asymptotics in the shadow zone
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1984
SP - 6
EP - 17
VL - 140
UR - http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a0/
LA - ru
ID - ZNSL_1984_140_a0
ER -
%0 Journal Article
%A V. M. Babich
%A V. P. Smyshlyaev
%T Scattering problem for the Schrödinger equation in the case of a potential linear in time and coordinate. I. Asymptotics in the shadow zone
%J Zapiski Nauchnykh Seminarov POMI
%D 1984
%P 6-17
%V 140
%U http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a0/
%G ru
%F ZNSL_1984_140_a0
The formal asymptotics of the scattering problem for the Schrödinger equation with a linear potential as $x+|t|\to+\infty$ is studied. In the shadow zone a formal asymptotic expansion is constructed which is matched with the known asymptotics as $t\to-\infty$. The expansion constructed loses asymptotic character near the curve $x=\frac16t^3$ (in the so-called projector zone). An assumption regarding the analogous behavior of the asymptotic series in the projector zone makes it possible to construct an expansion in the post-projection zone which goes over into the formulas for creeping waves.
