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...
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| Date: | 2023 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1013 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | 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 |
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