Extended C = ∞ conformal systems from classical Toda field theories

In a recent article (1988) we showed that the bosonic Toda field theories obey extended Virasoro symmetries which involve generators of spins higher than two; and that their quantization gives a systematic treatment of generalized conformal bosonic models. Their Virasoro central charges are such that they become infinite in the classical limit. This latter situation is studied in detail in the present paper, where a simple form of the general solution of the Toda field equations is given, that allows one to separate the modes and to study the Poisson bracket structure of the generators of the extended symmetry in a systematic way. Besides its relevance to the study of integrable classical systems this paves the way to the quantum case, already discussed by the authors and to be worked out in full detail in a separate publication. (orig.)