On the Construction and Integration of a Hierarchy for the Kaup System with a Self-Consistent Source in the Class of Periodic Functions

Автор(и)

  • A. Yakhshimuratov Urgench Branch of Tashkent University of Information Technologies named after Muhammad Al-Khwarizmi Al-Khwarizmi street
  • T. Kriecherbauer Bayreuth University, 95440, Bayreuth, Germany
  • B. Babajanov Urgench State University, H. Alimdjan 14, 220100, Urgench, Uzbekistan

DOI:

https://doi.org/10.15407/mag17.02.233

Ключові слова:

система рівнянь Каупа, ієрархія, самоузгоджене джерело, квадратичний пучок рівнянь Штурма-Ліувілля, обернена спектральна задача, формули слідів, періодичний потенціал

Анотація

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

Посилання

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Yakhshimuratov, A.; Kriecherbauer, T.; Babajanov, B. On the Construction and Integration of a Hierarchy for the Kaup System with a Self-Consistent Source in the Class of Periodic Functions. Журн. мат. фіз. анал. геом. 2021, 17, 233-257.

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