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

Jingzhu Wu, Xiuzhi Xing and Xianguo Geng

Advances in Mathematical Physics, 2015, vol. 2015, 1-9

Abstract:

The relations between -operators and multidimensional binary Bell polynomials are explored and applied to construct the bilinear forms with -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 -operators and a general Riemann theta function in terms of the Hirota method, which illustrate that bilinear -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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:291804

DOI: 10.1155/2015/291804

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