Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation

The relations between Dp-operators and multidimensional binary Bell polynomials are explored and applied to construct the bilinear forms with Dp-operators of nonlinear equations directly and quickly. Exact periodic wave solution of a (3+1)-dimensional generalized shallow water equation is obtained w...

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Bibliographic Details
Main Authors: Jingzhu Wu, Xiuzhi Xing, Xianguo Geng
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2015/291804
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Summary:The relations between Dp-operators and multidimensional binary Bell polynomials are explored and applied to construct the bilinear forms with Dp-operators of nonlinear equations directly and quickly. Exact periodic wave solution of a (3+1)-dimensional generalized shallow water equation is obtained with the help of the Dp-operators and a general Riemann theta function in terms of the Hirota method, which illustrate that bilinear Dp-operators can provide a method for seeking exact periodic solutions of nonlinear integrable equations. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.
ISSN:1687-9120
1687-9139