On the Construction and Integration of a Hierarchy for the Kaup System with a Self-Consistent Source in the Class of Periodic Functions
DOI:
https://doi.org/10.15407/mag17.02.233Анотація
У цій статті ми виводимо багату ієрархію для системи Каупа iз самоузгодженим джерелом в класі періодичних функцій. Ми обговорюємо повну інтегровність побудованих систем, яка заснована на трансформуванні у спектральні дані асоційованого квадратичного пучка рівнянь Штурма–Ліувілля з перiодичними коефіцієнтами. Зокрема, одержано рiвняння типу Дубровіна для часової еволюції спектральних даних для розв’язкiв будь-якої системи в ієрархії. Крім того, на прикладі окремої системи з ієрархії ми демонструємо переваги інтегровності, доводячи існування глобальних розв'язків для задачі Коші та надаючи явний розв'язок.Mathematics Subject Classification: 39A23, 35Q51, 34K13, 34K29
Ключові слова:
система рівнянь Каупа, ієрархія, самоузгоджене джерело, квадратичний пучок рівнянь Штурма-Ліувілля, обернена спектральна задача, формули слідів, періодичний потенціалПосилання
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