Complex parabolic subgroups of \(G_ 2\) and nonlinear differential equations (Q1084242)

The authors determine differential equations with superposition formulas corresponding to the exceptional Lie group \(G_ 2(C)\) and its two maximal parabolic subgroups. These equations have polynomial nonlinearities of order 2 in one case and of order 4 in the other. The authors propose to investigate other maximal subgroups of \(G_ 2(C)\), \(G_ 2^{NC}(R)\), and \(G_ 2^ C(R)\) in future work.