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arXiv · 2108.02171

Lie remarkable partial differential equations characterized by Lie algebras of point symmetries

Matteo Gorgone·Francesco Oliveri
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Abstract

Within the framework of inverse Lie problem, we give some non-trivial examples of coupled Lie remarkable equations, \textit{i.e.}, classes of differential equations that are in correspondence with their Lie point symmetries. In particular, we determine hierarchies of second order partial differential equations uniquely characterized by affine transformations of $\mathbb{R}^{n+m}$, and a system of two third order partial differential equations in two independent variables uniquely determined by the Lie algebra of projective transformations of $\mathbb{R}^4$.

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Matteo Gorgone, Francesco Oliveri. 2021-08-02. Lie remarkable partial differential equations characterized by Lie algebras of point symmetries. https://doi.org/10.1016/j.geomphys.2019.06.011

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