Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation-Reference-Cited by-同舟云学术

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

Published:2015 Issue: Volume:2015 Page:1-9
ISSN:1687-9120
Container-title:Advances in Mathematical Physics
language:en
Short-container-title:Advances in Mathematical Physics

Author:

Wu Jingzhu¹,Xing Xiuzhi¹,Geng Xianguo²

Affiliation:

1. Department of Mathematics, Zhoukou Normal University, Zhoukou 466000, China

2. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China

Abstract

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

Publisher

Hindawi Limited

Subject

Applied Mathematics,General Physics and Astronomy

Link

http://downloads.hindawi.com/journals/amp/2015/291804.pdf

Reference24 articles.

1. Painlevé analysis, auto-Bäcklund transformation and new analytic solutions for a generalized variable-coefficient Korteweg-de Vries (KdV) equation

2. Pseudopotentials, Lax Pairs and Bäcklund Transformations for Generalized Fifth-Order KdV Equation

3. New Bilinear Bäcklund Transformation and Lax Pair for the Supersymmetric Two-Boson Equation

4. Broer-Kaup Systems from Darboux Transformation Related Symmetry Constraints of Kadomtsev-Petviashvili Equation

5. The Bäcklund and Inverse Scattering Transform of the K-dV Equation with Nonuniformities

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