Reduction of a Class of Nonlinear Integral Equations to a Cauchy System

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Abstract
It is shown that a wide class of nonlinear integral equations can be transformed into a Cauchy system. Then it is shown that a solution of the Cauchy system provides a solution of the original nonlinear integral equation. Such reductions are important because modern computers can solve initial value problems with speed and accuracy. There are intended applications in the theories of multiple scattering, optimal filtering, and lateral inhibition of neural systems. This new approach makes no use of successive approximations or series expansions.