Abstract:We consider the one dimensional space-periodic Vlasov-Poisson equations and construct, close to symmetric flat velocity strips, small amplitude traveling quasi-periodic electron-layers, namely strip-shaped patches of electrons in the phase space. These solutions are found for most values of the strip area. The proof uses a Nash-Moser construction together with reducibility arguments based on pseudo-differential homogeneous expansions and KAM reductions. Thanks to a suitable linear transformation of the unknowns, we reveal a connection between the electron patch problem and the classical, physically relevant, electronic Euler-Poisson system with cubic pressure law. As a direct, non trivial consequence, we obtain small-amplitude quasi-periodic traveling waves for this model as well. To the best of our knowledge, this work provides the first rigorous example of construction of quasi-periodic solutions for kinetic models.
| Comments: | 81 pages |
| Subjects: | Analysis of PDEs (math.AP); Plasma Physics (physics.plasm-ph) |
| Cite as: | arXiv:2605.25885 [math.AP] |
| (or arXiv:2605.25885v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25885 arXiv-issued DOI via DataCite (pending registration) |
From: Emeric Roulley [view email]
[v1]
Mon, 25 May 2026 14:15:01 UTC (120 KB)
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