Associated transforms for solution of nonlinear equations

Abstract

Nonlinear multivariable differential or integrodifferential equations with terms of mixed dimensionality can be solved using multidimensional Laplace transform. The special technique used to find the inverse of the multidimensional Laplace transform is known as the association of variables. In this paper, some basic theorems are developed for the theory of association. Examples are presented for each theorem. Once the basic theorems are established, it is possible to derive many useful ssociated pairs.