Long-time asymptotics for Toda shock waves in the modulation region
We show that a Toda shock wave is asymptotically close to a modulated finite gap solution in the right modulation region. We previously derived formulas for the leading terms of the asymptotic expansion of this shock wave in all five principal regions and conjectured that in two modulation regions t...
Збережено в:
| Дата: | 2023 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
|
| Теми: | |
| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1013 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| Резюме: | We show that a Toda shock wave is asymptotically close to a modulated finite gap solution in the right modulation region. We previously derived formulas for the leading terms of the asymptotic expansion of this shock wave in all five principal regions and conjectured that in two modulation regions the next term is of order $O(t^{-1})$. In the present paper we prove this fact and investigate how resonances and eigenvalues influence the leading asymptotic behaviour. Our main contribution is the solution of the local parametrix Riemann-Hilbert problems and a rigorous justification of the analysis. In particular, this involves the construction of a proper singular matrix model solution.
Mathematical Subject Classification 2020: 37K40, 35Q53, 37K45, 35Q15 |
|---|