Link to actual problem [11326]
type detected by program
{"unknown"}
type detected by Maple
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{x^{3} y}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y^{2} x^{3}}{2}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{x^{2} y}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y^{2} x^{2}}{2}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{y x}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {x y^{2}}{2}\right ] \\ \end{align*}