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The scattering transform for the two-dimensional Schrodinger operator with a potential that decreases at infinity at fixed nonzero energyстатья
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 13 января 2015 г.
- Автор: Grinevich P.G.
- Журнал: Russian Mathematical Surveys
- Том: 55
- Номер: 6
- Год издания: 2000
- Издательство: Turpion - Moscow Ltd.
- Местоположение издательства: United Kingdom
- Первая страница: 1015
- Последняя страница: 1083
- DOI: 10.1070/RM2000v055n06ABEH000333
- Аннотация: 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.
- Добавил в систему: Гриневич Петр Георгиевич