Inverse Scattering Theory for Schrödinger Operators with Steplike Potentials
DOI:
https://doi.org/10.15407/mag11.02.123Анотація
Вивчаються пряма та обернена задачі розсіювання для одновимірного рівняння Шредінгера із потенціалами типу сходинки. Встановлюються необхідні та достатні умови на дані розсіювання, що відповідають потенціалу із заданими гладкістю та швидкістю збігання до своїх асимптот. Отримані результати узагальнюють раніше відомі та є важливими для розв'язання задачі Коші для рівняння Кортевега-де Фріза методом оберненої задачі розсіювання.
Mathematics Subject Classification: 34L25, 81U40, 34B30, 34L40.
Ключові слова:
оператор Шредінгера, обернена задача розсіювання, потенціал типу сходинкиПосилання
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