Symmetry Classification of quasi-linear PDE's. II: an exceptional case

TL;DR

This paper completes the symmetry classification of certain quasi-linear PDEs by identifying an exceptional Lie symmetry that appears under specific parameter conditions, leading to solutions relevant in plasma physics.

Contribution

It introduces an analysis of an exceptional Lie point symmetry in quasi-linear PDEs, revealing conditions under which it exists and its implications for plasma physics solutions.

Findings

Identification of an exceptional Lie symmetry under specific parameter constraints

Connection of the symmetry to plasma physics solutions

Example of a conditional symmetry of weak type

Abstract

This short note completes the symmetry analysis of a class of quasi-linear partial differential equations considered in the previous paper (Nonlinear Dynamics, Vol. 51, 309-316 (2008)): it deals with the presence of an "exceptional" Lie point symmetry, not previously examined, which is admitted only if the involved parameters are fixed by precise relationships. The peculiarity of this symmetry is enhanced by the fact that it leads to a solution relevant in the theory of plasma physics, and also related to the presence of a nontrivial example of a conditional symmetry of weak type.