The Generalized Marchenko Method in the Inverse Scattering Problem for a First-Order Linear System with Energy-Dependent Potentials
DOI:
https://doi.org/10.15407/mag19.01.003Анотація
Метод Марченка розповсюджено на обернену задачу розсiювання для системи лiнiйних диференцiальних рiвнянь першого порядку, якi мiстять потенцiали пропорцiйнi спектральному параметру. Вiдповiдну систему iнтегральних рiвнянь Марченка одержано таким чином, що цей метод може бути застосованим до певних систем, для яких ранiше застосування методу Марченка було неможливим. Показано як потенцiали i розв’язки Йоста лiнiйної системи будуються з розв’язкiв системи Марченка. Iнформацiя про зв’язанi стани для лiнiйної системи з будь-якою кiлькiстю зв’язаних станiв i будь-якими кратностями описана в термiнах пари трiйок сталих матриць. У випадку, коли потенцiали в лiнiйнiй системi є безвiдбивними, знайдено деякi формули явних розв’язкiв в замкненiй формi для потенцiалiв i для розв’язкiв Йоста лiнiйної системи. Теорiя iлюстрована деякими явними прикладами.
Mathematical Subject Classification 2020: 34A55, 34L25, 34L40, 47A40
Ключові слова:
метод Марченка, узагальнене iнтегральне рiвняння Марченка, зворотнє розсiювання, лiнiйна система першого порядку, енергетично залежний потенцiал, розв’язки ЙостаПосилання
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