Long-time asymptotics for Toda shock waves in the modulation region
DOI:
https://doi.org/10.15407/mag19.02.396Анотація
Ми показуємо, що хвиля стиснення для ланцюжка Тоди є асимптотично наближеною до модульованого скiнченнозонного розв’язку у правому модуляцiйному регiонi. Ранiше нами було виведено формули для головних членiв асимптотичного розвинення цiєї хвилi стиснення в усiх п’ятьох принципових регiонах, а також було припущено, що у двох модуляцiйних регiонах наступний член є порядку $O(t^{-1})$. У данiй роботi ми доводимо цей факт i дослiджуємо, як дискретний спектр та резонанси впливають на провiдну асимптотику. Основним внеском є розв’язання локальних задач Рiмана–Гiльберта (задач параметрiксу) i строге обґрунтування заключного асимптотичного аналiзу. Зокрема, це включає в себе побудову належного матричного розв’язку модельної задачi Рiмана–Гiльберта.
Mathematical Subject Classification 2020: 37K40, 35Q53, 37K45, 35Q15
Ключові слова:
Рiвняння Тоди, задача Рiмана–Гiльберта, тип сходинки, хвиля стисненняПосилання
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