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A Paley-Wiener Theorem for Periodic Scattering with Applications to the Korteweg-de Vries Equation
Репозиторій DSpace/Manakin
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A Paley-Wiener Theorem for Periodic Scattering with Applications to the Korteweg-de Vries Equation
Посилання:
A Paley-Wiener Theorem for Periodic Scattering with Applications to the Korteweg-de Vries Equation / I. Egorova, G. Teschl // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 1. — С. 21-33. — Бібліогр.: 24 назв. — англ.
Підтримка:
We are very grateful to F. Gesztesy for hints with respect to the literature. G. Teschl gratefully acknowledges the stimulating atmosphere at the Centre for Advanced Study at the Norwegian Academy of Sciences and Letters in Oslo during June 2009 where parts of this paper were written as a part of the international research program on Nonlinear Partial Differential Equations.
Дата:
2010
Переглядів:
799
Завантажень:
517
Анотація:
A one-dimensional SchrÄodinger operator which is a short-range perturbation of a finite-gap operator is considered. There are given the necessary and su±cient conditions on the left/right reflection coeffcient such that the difference of the potentials has finite support to the left/right, respectively. Moreover, these results are applied to show a unique continuation type result for solutions of the Korteweg{de Vries equation in this context. By virtue of the Miura transform an analogous result for the modified Korteweg-de Vries equation is also obtained.
