Lie Group Analysis of a Forced KdV Equation

Table 2

Table of commutators.

[𝑋𝑖,𝑋𝑗]	𝑋1	𝑋2	𝑋3
𝑋1	0	0	𝛼𝑋1
𝑋2	0	0	−3𝑛𝛼^2𝑋1−2𝛼𝑋2
𝑋3	−𝛼𝑋1	3𝑛𝛼^2𝑋1+2𝛼𝑋2	0

Here [𝑋_𝑖,𝑋_𝑗]=𝑋_𝑖(𝑋_𝑗)−𝑋_𝑗(𝑋_𝑖);𝑖,𝑗=1,2,3 is the commutator operation.