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It is well-known that Toda systems (Toda field theory) can possess different algebraic structure based on Cartan Matrix in the Hamiltonian's potential.

But all solutions I have seen were written only for either Liouville (trivial) case or $A_2$ algebra.

I wonder if there exist (analytical) solutions for other (semi-) simple Lie algebras, e.g. $B_2, G_2, D_2$ (and higher dimensional if possible).

Thank you.

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