Trace formulas and continuous dependence of spectra for the periodic conservative Camassa–Holm flow
| Autor: | Noema Nicolussi, Aleksey Kostenko, Jonathan Eckhardt |
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| Rok vydání: | 2020 |
| Předmět: |
Floquet theory
Trace (linear algebra) Applied Mathematics 010102 general mathematics Spectrum (functional analysis) 01 natural sciences Spectral line Mathematics - Spectral Theory 010101 applied mathematics Isospectral Distribution (mathematics) Primary 34L05 34B07 Secondary 34L15 37K15 Flow (mathematics) Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics 0101 mathematics Spectral Theory (math.SP) Borel measure Analysis Mathematical physics Mathematics |
| Zdroj: | Journal of Differential Equations. 268:3016-3034 |
| ISSN: | 0022-0396 |
| Popis: | This article is concerned with the isospectral problem \[ -f'' + \frac{1}{4} f = z\omega f + z^2 \upsilon f \] for the periodic conservative Camassa-Holm flow, where $\omega$ is a periodic real distribution in $H^{-1}_{\mathrm{loc}}(\mathbb{R})$ and $\upsilon$ is a periodic non-negative Borel measure on $\mathbb{R}$. We develop basic Floquet theory for this problem, derive trace formulas for the associated spectra and establish continuous dependence of these spectra on the coefficients with respect to a weak$^\ast$ topology. Comment: 16 pages. arXiv admin note: text overlap with arXiv:1801.04612 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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