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arXiv · 2610.20672

The \textsc{ABC}-equation revisited: missed integrable cases. Part I: classification and (quasi) integrable structures

I. S. Krasil'shchik
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Abstract

We consider the \textsc{ABC}-equation $Au_xu_{yt} + Bu_yu_{xt} + Cu_tu_{xy} = 0$, $A$, $B$, $C\in\mathbb{R}$, which was proved to be integrable in the case $A + B + C = 0$ (the Veronese web equation). Our study reveals ten more cases that admit integrable structures that, to the best of our knowledge, where not known before. The techniques is based essentially on the theory of the tangent and cotangent coverings.

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I. S. Krasil'shchik. 2026-10-14. The \textsc{ABC}-equation revisited: missed integrable cases. Part I: classification and (quasi) integrable structures. https://arxiv.org/abs/2610.20672

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