Geodesic
Scattering transformation at fixed non-zero energy for the two-dimensional Schr\"odinger operator with potential decaying at infinity
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 55 (2000) no. 6, pp. 1015-1083

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

We study the problem of reconstructing the potential of the two-dimensional Schrödinger operator from scattering data measured at fixed energy. This problem, in contrast to the general multidimensional inverse problem, possesses an infinite-dimensional symmetry algebra generated by the Novikov–Veselov hierarchy and hence is “exactly soluble” in some sense; the complexity of the answer is approximately the same as in the one-dimensional problem. We make heavy use of methods developed in modern soliton theory. Since the quantum fixed-energy scattering problem is mathematically equivalent to the acoustic single-frequency scattering problem, we see that the results of the present paper apply in both cases. 
@article{RM_2000_55_6_a0,
     author = {P. G. Grinevich},
     title = {Scattering transformation at fixed non-zero energy for the two-dimensional {Schr\"odinger} operator with potential decaying at infinity},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {1015--1083},
     publisher = {mathdoc},
     volume = {55},
     number = {6},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2000_55_6_a0/}
}
TY  - JOUR
AU  - P. G. Grinevich
TI  - Scattering transformation at fixed non-zero energy for the two-dimensional Schr\"odinger operator with potential decaying at infinity
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2000
SP  - 1015
EP  - 1083
VL  - 55
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_2000_55_6_a0/
LA  - en
ID  - RM_2000_55_6_a0
ER  - 
%0 Journal Article
%A P. G. Grinevich
%T Scattering transformation at fixed non-zero energy for the two-dimensional Schr\"odinger operator with potential decaying at infinity
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2000
%P 1015-1083
%V 55
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_2000_55_6_a0/
%G en
%F RM_2000_55_6_a0
P. G. Grinevich. Scattering transformation at fixed non-zero energy for the two-dimensional Schr\"odinger operator with potential decaying at infinity. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 55 (2000) no. 6, pp. 1015-1083. http://geodesic.mathdoc.fr/item/RM_2000_55_6_a0/