Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra

Автор(и)

  • Iryna Egorova B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
  • Johanna Michor Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
  • Gerald Teschl Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

DOI:

https://doi.org/10.15407/mag14.04.406

Ключові слова:

ланцюжок Тоди, проблема Рімана-Гільберта, хвиля стиску

Анотація

Застосовуючи нелінійний аналіз найшвидшого спуску для осциляторної задачі факторизації Рімана–Гільберта, ми виводимо асимптотики при великих значеннях часу для хвилі стиску ланцюжка Тоди. Ми демонструємо, що півплощина просторової/часової змінних розпадається на п'ять основних областей. У двох зовнішніх розв'язок є асимптотично наближеним до відповідних вільних тонів. У середньому регіоні він є наближеним до двозонного розв'язку ланцюжка Тоди. У двох регіонах, що залишилися, розв'язок є асимптотично наближеним до повільно модульованої еліптичної хвилі. Зокрема, форма розв'язку в цих областях підтверджує гіпотезу Вернакідеса, Дейфта та Оба від 1991 р.

Mathematics Subject Classification: 37K40, 37K10, 37K60, 35Q15.

Посилання

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Egorova, I.; Michor, J.; Teschl, G. Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra. Журн. мат. фіз. анал. геом. 2018, 14, 406-451.

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