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Journal of Applied Mathematics
Volume 2013, Article ID 518415, 10 pages
Research Article

Peaked and Smooth Solitons for Equation

School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China

Received 6 August 2013; Revised 10 October 2013; Accepted 8 November 2013

Academic Editor: Alberto Cabada

Copyright © 2013 Yongan Xie 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.


This paper is contributed to explore all possible single peak solutions for the equation . Our procedure shows that the equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal or possesses compacton solutions only when . We present a new smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of the equation.