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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 173192, 5 pages
Research Article

The Lagrangian, Self-Adjointness, and Conserved Quantities for a Generalized Regularized Long-Wave Equation

Department of Mathematics, Hangzhou Dianzi University, Zhejiang 310018, China

Received 9 January 2014; Accepted 2 May 2014; Published 8 May 2014

Academic Editor: Tiecheng Xia

Copyright © 2014 Long Wei and Yang Wang. 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.


We consider the Lagrangian and the self-adjointness of a generalized regularized long-wave equation and its transformed equation. We show that the third-order equation has a nonlocal Lagrangian with an auxiliary function and is strictly self-adjoint; its transformed equation is nonlinearly self-adjoint and the minimal order of the differential substitution is equal to one. Then by Ibragimov’s theorem on conservation laws we obtain some conserved qualities of the generalized regularized long-wave equation.