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This paper presents a new transform calculus for analyzing a certain class of nonlinear systems. The method, which can be justified rigorously by the partition theory, essentially transforms a nonlinear differential equation having certain conditions imposed on its linear, nonlinear, and driving terms into an algebraic equation. The latter is easily solved recursively owing to its symmetry and convolution...
The Taylor-Cauchy transform for the analysis of nonlinear systems was presented at the 1959 IRE National Convention. In this paper it is shown that the Laurent-Cauchy transform can be derived from the Taylor-Cauchy transform by a simple mapping. Whereas a complex ? plane is used in the Taylor-Cauchy transform, a complex ? plane is used in the Laurent-Cauchy trans-form where the two complex variables...
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