Nonlinear first order partial differential equations reducible to first order homogeneous and autonomous quasilinear ones

Abstract

A theorem providing necessary conditions enabling one to map a nonlinear system of first order partial differential equations to an equivalent first order autonomous and homogeneous quasilinear system is given. The reduction to quasilinear form is performed by constructing the canonical variables associated to the Lie point symmetries admitted by the nonlinear system. Some applications to relevant partial differential equations are given.

16 pages, no figures

Cited by in corpus (4)

• A Consistent Approach to Approximate Lie Symmetries of Differential Equations
• Lie remarkable partial differential equations characterized by Lie algebras of point symmetries
• Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives
• Approximately invariant solutions of creeping flow equations