Recurrence relations in the solution of a certain class of nonlinear systems

This paper (a modified version of the material in an unpublished paper of the same name by the author presented at the AIEE 1957 Summer General Meeting) introduces aspects of a generalized mathematical theory for the analysis of a certain class of nonlinear systems. (Since the original presentation of this paper other work has appeared,1??5 which enlarges on the comments made here and extends the present work.) It is shown that under a very broad class of conditions, consistent with physical realization, a class of systems exists for which it is possible to develop exact and unique mathematical solutions. These conditions are important since nonlinear differential equations do not in general possess such unique properties although linear differential equations do.