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

TL;DR

This paper presents a theorem that provides necessary conditions for transforming certain nonlinear first order PDE systems into equivalent first order autonomous and homogeneous quasilinear systems using Lie symmetries, with applications to important PDEs.

Contribution

It introduces a theorem that enables the reduction of nonlinear PDE systems to quasilinear form via Lie symmetry analysis, offering a systematic approach for simplifying complex equations.

Findings

Reduction method via Lie symmetries demonstrated

Applications to relevant PDEs shown

Conditions for mapping nonlinear to quasilinear systems established

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.