Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows

Table 1

Commutators of the admitted symmetries.

[𝑋𝑖,𝑋𝑗]	𝑋1	𝑋2	𝑋3	𝑋4	𝑋5	𝑋6
𝑋1	0	0	0	2𝑋1	2𝑋3	4𝑋4−2𝑋2
𝑋2	0	0	0	0	0	0
𝑋3	0	0	0	𝑋3	−𝑋2	2𝑋5
𝑋4	−2𝑋1	0	−𝑋3	0	𝑋5	2𝑋6
𝑋5	−2𝑋3	0	𝑋2	−𝑋5	0	0
𝑋6	2𝑋2−4𝑋4	0	−2𝑋5	−2𝑋6	0	0