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Fast decaying potentials on the finite-gap background and the ∂-bar-problem on the Riemann surfacesстатья
Информация о цитировании статьи получена из
Scopus,
Web of Science
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: Theoretical and Mathematical Physics
- Том: 99
- Год издания: 1994
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 599
- Последняя страница: 605
- DOI: 10.1007/BF01016145
- Аннотация: The direct and the inverse ‘scattering problems’ for the heat-conductivity operator TeX are studied for the following class of potentials:u(x,y)=u_0 (x,y)+u_1(x,y), where u_0(x,y) is a nonsingular real finite-gap potential and u_1(x,y) decays sufficiently fast as x^2+y^2→∞. We show that the ‘scattering data’ for such potentials is the TeX data on the Riemann surface corresponding to the potential u_0 (x,y). The ‘scattering data’ corresponding to real potentials is characterized and it is proved that the inverse problem corresponding to such data has a unique nonsingular solution without the ‘small norm’ assumption. Analogs of these results for the fixed negative energy scattering problem for the two-dimensional time-independent Schrödinger operator are obtained.
- Добавил в систему: Гриневич Петр Георгиевич