Global Actions of the Lie Symmetries of the Nonlinear Filtration Equation

TL;DR

This paper classifies the Lie point symmetries of the nonlinear filtration equation, demonstrating their global actions in most cases and identifying limitations in one special case.

Contribution

It provides a detailed classification of symmetries and shows how they exponentiate to global group actions, with specific results on when globalization is possible.

Findings

Lie symmetries are global in the generic and two special cases

Symmetries form a solvable Lie group in these cases

Globalization fails in the third special case

Abstract

The classification of the Lie point symmetries of the nonlinear filtration equation gives the generic case and three special cases. By restricting to a special class of functions, we show that the Lie symmetries of the nonlinear filtration equation exponentiate to a global action of a solvable Lie group in the generic case and two of the three special cases. We show that the action of the Lie point symmetries cannot be globalized for the third special case.