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Mathematical Problems in Engineering
Volume 2006, Article ID 97020, 11 pages
http://dx.doi.org/10.1155/MPE/2006/97020

On the RF-pair operations for the exact solution of some classes of nonlinear Volterra integral equations

1Department of Mathematics, Urmia University, P.O. Box 165, Urmia, Iran
2Department of Mathematics, K. N. Toosi University of Technology, Tehran 16315, Iran
3Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran

Received 1 May 2005; Revised 17 November 2005; Accepted 15 January 2006

Copyright © 2006 P. Darania and M. Hadizadeh. 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.

Abstract

We study the exact solution of some classes of nonlinear integral equations by series of some invertible transformations and RF-pair operations. We show that this method applies to several classes of nonlinear Volterra integral equations as well and give some useful invertible transformations for converting these equations into differential equations of Emden-Fowler type. As a consequence, we analyze the effect of the proposed operations on the exact solution of the transformed equation in order to find the exact solution of the original equation. Some applications of the method are also given. This approach is effective to find a great number of new integrable equations, which thus far, could not be integrated using the classical methods.