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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 2825416, 9 pages
https://doi.org/10.1155/2017/2825416
Research Article

Third-Order Conditional Lie–Bäcklund Symmetries of Nonlinear Reaction-Diffusion Equations

1College of Information and Management Science, Henan Agricultural University, Zhengzhou 450046, China
2College of Information Science and Technology, Donghua University, Shanghai 201620, China

Correspondence should be addressed to Keqin Su; moc.liamtoh@usniqek

Received 24 October 2016; Revised 16 January 2017; Accepted 18 January 2017; Published 9 February 2017

Academic Editor: Nikos Mastorakis

Copyright © 2017 Keqin Su and Jie Cao. 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

The third-order conditional Lie–Bäcklund symmetries of nonlinear reaction-diffusion equations are constructed due to the method of linear determining equations. As a consequence, the exact solutions of the resulting equations are derived due to the compatibility of the governing equations and the admitted differential constraints, which are resting on the characteristic of the admitted conditional Lie–Bäcklund symmetries to be zero.