International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 177-190

Associated transforms for solution of nonlinear equations

Joyati Debnath1,2 and Narayan C. Debnath1,2

1Department of Mathematics and Computer Science, University of Wisconsin, River Rills 54022, WI, USA
2Department of Mathematics and Computer Science, Winona State University, Winona, MN, USA

Copyright © 1991 Joyati Debnath and Narayan C. Debnath. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.