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Table 1 Table of Lie brackets

From: Construction of invariant solutions and conservation laws to the \((2+1)\)-dimensional integrable coupling of the KdV equation

\([X_{i},X_{j}]\) \(X_{1}\) \(X_{2}\) \(X_{3}\) \(X_{4}\) \(X_{5}\)
\(X_{1}\) 0 \(-X_{2}\) \(-\frac{1}{3}X_{3}\) 0 0
\(X_{2}\) \(X_{2}\) 0 0 0 0
\(X_{3}\) \(\frac{1}{3}X_{3}\) 0 0 0 0
\(X_{4}\) 0 0 0 0 \(-X_{5}\)
\(X_{5}\) 0 0 0 \(X_{5}\) 0