Inverse Scattering Theory for Schrödinger Operators with Steplike Potentials

Автор(и)

  • I. Egorova B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv 61103, Ukraine
    Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Wien 1090, Austria
  • Z. Gladka B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv 61103, Ukraine
  • T. L. Lange Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Wien 1090, Austria
  • G. Teschl Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Wien 1090, Austria
    International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, Wien 1090, Austria

DOI:

https://doi.org/10.15407/mag11.02.123

Ключові слова:

оператор Шредінгера, обернена задача розсіювання, потенціал типу сходинки

Анотація

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.

Посилання

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Egorova, I.; Gladka, Z.; Lange, T. L.; Teschl, G. Inverse Scattering Theory for Schrödinger Operators with Steplike Potentials. Журн. мат. фіз. анал. геом. 2015, 11, 123-158.

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