Lie symmetries of a system arising in plasma physics

Abstract

Lie group classification for a diffusion‐type system that has applications in plasma physics is derived. The classification depends on the values of 5 parameters that appear in the system. Similarity reductions are presented. Certain initial value problems are reduced to problems with the governing equations being ordinary differential equations. Examples of potential symmetries are also presented.

Special transformation properties for certain equations with applications in Plasma Physics

“…An important benefit of the potential symmetry analysis is the disclosure of linearizing mappings. Lie symmetry analysis of the nonlinear system () did not provide such mappings 4 . However, in this work we have shown that some of its auxiliary systems admit infinite dimensional symmetries that lead to linearizing mappings.…”

“…Here we continue the work of Charalambous and Sophocleous, 4 where Lie symmetries of the system () were classified. Our goal is to derive nonlocal symmetries and other nonlocal transformations.…”

“…Both equations in the system (1) are written in a conserved form. By introducing the potential variable w we obtain the auxiliary system (3) and introducing the potential variable z we obtain the auxiliary system (4). The introduction of both potential variables w and z leads to the potential system (5).…”

“…Examples of potential symmetries for the system (1) are presented in Charalambous and Sophocleous. 4 Both equations in the system (1) are written in conserved forms. If we introduce a potential variable w, the first equation can be written as a system of two equations.…”

“…To our knowledge, the previous works 8–11 are the only articles that consider the problem of deriving potential symmetries for systems. Examples of potential symmetries for the system () are presented in Charalambous and Sophocleous 4 …”