Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 908975, 15 pages
http://dx.doi.org/10.1155/2012/908975
Research Article

Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation

Hongwei Yang,1,2,3,4 Yunlong Shi,2 Baoshu Yin,1,4 and Huanhe Dong2

1Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
2College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China
3Graduate School, Chinese Academy of Sciences, Beijing 100049, China
4Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao 266071, China

Received 20 June 2012; Accepted 22 August 2012

Academic Editor: Ramajayam Sahadevan

Copyright © 2012 Hongwei Yang et al. 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 discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.