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

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 ${\mathbb{R}}^4$.

arXiv comment22 pages

References in corpus (3)

• Ordinary differential equations described by their Lie symmetry algebra
• Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives
• Nonlinear first order partial differential equations reducible to first order homogeneous and autonomous quasilinear ones

Cited by in corpus (5)

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• Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation
• Hidden symmetries, hidden conservation laws and exact solutions of dispersionless Nyzhnyk equation