Theory and Modern Applications
Table 2 Adjoint representation table of Eq. (1)
From: Lie symmetry and μ-symmetry methods for nonlinear generalized Camassa–Holm equation
\(\operatorname{Ad}(\exp (\varepsilon {\nu }_{i}){\nu }_{j})\) | \({\nu }_{1}\) | \({\nu }_{2}\) | \({\nu }_{3}\) |
|---|---|---|---|
\({\nu }_{1}\) | \({\nu }_{1}\) | \({\nu }_{2}\) | \({\nu }_{3}\) |
\({\nu }_{2}\) | \({\nu }_{1}\) | \({\nu }_{2}\) | \(\nu _{3}-\varepsilon {\nu }_{2} \) |
\({\nu }_{3}\) | \({\nu }_{1}\) | \({\nu }_{2}+\varepsilon {\nu }_{2}\) | \({\nu }_{3}\) |