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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 342680, 12 pages
http://dx.doi.org/10.1155/2012/342680
Research Article

Lie Groups Analysis and Contact Transformations for Ito System

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80303, Jeddah 21589, Saudi Arabia

Received 12 May 2012; Accepted 10 September 2012

Academic Editor: Ahmed El-Sayed

Copyright © 2012 M. M. Al-Shomrani. 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

Generalized Ito systems of four coupled nonlinear evaluation equations are proposed. New classes of exact invariant solutions by using Lie group analysis are obtained. Moreover, we investigate the existence of a one-parameter group of contact transformations for a generalized Ito system. Consequently, we study the relationship between one-parameter group of a contact transformation and a one-parameter Lie point transformation for a generalized Ito system.