Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation. (10th September 2015)

• Record Type: Journal Article
• Authors: Wu, Jingzhu; Xing, Xiuzhi; Geng, Xianguo
• Other Names: Hounkonnou Mahouton N. Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2015(2015)
• Publication Date: 2015-09-10
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2015/291804
• Languages: English
• ISSNs: 1687-9120

Abstract

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