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

22 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 (2)

• Thermodynamical analysis and constitutive equations for a mixture of viscous Korteweg fluids
• On the characterization of constitutive equations for third grade viscous Korteweg fluids