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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/291804 |
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| _version_ | 1850172572518318080 |
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| author | Jingzhu Wu Xiuzhi Xing Xianguo Geng |
| author_facet | Jingzhu Wu Xiuzhi Xing Xianguo Geng |
| author_sort | Jingzhu Wu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d0132d0d0bc942879e68649b656c885d |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-d0132d0d0bc942879e68649b656c885d2025-08-20T02:20:03ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/291804291804Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water EquationJingzhu Wu0Xiuzhi Xing1Xianguo Geng2Department of Mathematics, Zhoukou Normal University, Zhoukou 466000, ChinaDepartment of Mathematics, Zhoukou Normal University, Zhoukou 466000, ChinaDepartment of Mathematics, Zhengzhou University, Zhengzhou 450052, ChinaThe 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.http://dx.doi.org/10.1155/2015/291804 |
| spellingShingle | Jingzhu Wu Xiuzhi Xing Xianguo Geng Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation Advances in Mathematical Physics |
| title | Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation |
| title_full | Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation |
| title_fullStr | Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation |
| title_full_unstemmed | Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation |
| title_short | Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation |
| title_sort | generalized bilinear differential operators application in a 3 1 dimensional generalized shallow water equation |
| url | http://dx.doi.org/10.1155/2015/291804 |
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