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Inverse backscattering Born approximation for the magnetic Schrödinger equation in three dimensions
Author(s) -
Sandhu Jan,
Serov Valery
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2920
Subject(s) - mathematics , smoothness , born approximation , quadratic equation , series (stratigraphy) , term (time) , nonlinear system , mathematical analysis , operator (biology) , inverse , space (punctuation) , inverse scattering problem , inverse problem , mathematical physics , scattering , physics , quantum mechanics , geometry , paleontology , biochemistry , chemistry , linguistics , philosophy , repressor , gene , transcription factor , biology
The inverse backscattering Born approximation is studied for the three‐dimensional magnetic Schrödinger operator. Under the assumption that the Born series converges in the weighted spaceL − δ 2R 3, we calculate precisely the linear term and the first nonlinear (quadratic) term of this Born series. The estimation of smoothness of the first nonlinear term is also presented. Copyright © 2013 John Wiley & Sons, Ltd.