Abstract:We show that Hertling-Manin F-manifolds provide the appropriate theoretical framework for studying the integrability of quasilinear systems of first-order evolutionary partial differential equations of the form ${\bf u}_t=X\circ {\bf u}_x$ under the mild assumption that $X$ is a cyclic vector field with respect to the F-product $\circ$. This approach is very general and allows us to treat even non-regular systems that were previously beyond the scope of existing techniques. Like in the regular case the information about integrability is contained in a torsionless connection associated with the system and the integrability condition reduces to a geometric condition involving the Riemann tensor of the connection and the structure functions of the product.
| Comments: | 49 pages |
| Subjects: | Mathematical Physics (math-ph) |
| Cite as: | arXiv:2605.25277 [math-ph] |
| (or arXiv:2605.25277v1 [math-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25277 arXiv-issued DOI via DataCite (pending registration) |
From: Paolo Lorenzoni [view email]
[v1]
Sun, 24 May 2026 22:14:04 UTC (45 KB)
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