Table of Contents
ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 384906, 10 pages
http://dx.doi.org/10.5402/2012/384906
Research Article

Two Different Classes of Wronskian Conditions to a (3 + 1)-Dimensional Generalized Shallow Water Equation

Department of Applied Mathematics, Northwestern Polytechnical University, Shaanxi, Xi’an 710072, China

Received 4 June 2012; Accepted 19 June 2012

Academic Editors: G. L. Karakostas and T. Ozawa

Copyright © 2012 Yaning Tang and Pengpeng Su. 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

Based on the Hirota bilinear method and Wronskian technique, two different classes of sufficient conditions consisting of linear partial differential equations system are presented, which guarantee that the Wronskian determinant is a solution to the corresponding Hirota bilinear equation of a (3+1)-dimensional generalized shallow water equation. Our results show that the nonlinear equation possesses rich and diverse exact solutions such as rational solutions, solitons, negatons, and positons.