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arXiv · 2512.12789

Hyperbolic equations with fifth-order symmetries

Rustem N. Garifullin
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Abstract

This paper examines the classification of hyperbolic equations. We study a class of equations of the form $$\frac{\partial^2 u}{\partial x\partial y}=F\left(\frac{\partial u}{\partial x},\frac{\partial u}{\partial y},u\right),$$ where $u(x,y)$ is the unknown function and $x,y$ are independent variables. The classification is based on the requirement for the existence of higher fifth-order symmetries. As a result, a list of four equations with the required conditions was obtained.

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Rustem N. Garifullin. 2025-12-14. Hyperbolic equations with fifth-order symmetries. https://arxiv.org/abs/2512.12789

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