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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 714214, 11 pages
http://dx.doi.org/10.1155/2014/714214
Research Article

Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions

College of Mathematics, Chongqing Normal University, Chongqing 401331, China

Received 31 October 2013; Accepted 7 January 2014; Published 4 March 2014

Academic Editor: Zuo-nong Zhu

Copyright © 2014 Weiguo Rui. 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

By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.