Grammian and Pfaffian solutions as well as Pfattianization for a （3＋ 1 ）-dimensional generalized shallow water equation

Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a （3＋1）-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-...

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Published in中国物理B：英文版 Vol. 21; no. 7; pp. 85 - 91
Main Author 唐亚宁 马文秀 徐伟
Format Journal Article
LanguageEnglish
Published 2012
Subjects
双线性形式
广义
浅水方程
耦合系统
过程方程
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Summary:Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a （3＋1）-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented.
Bibliography:Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a （3＋1）-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented.
11-5639/O4
Tang Ya-Ning, Ma Wen-Xiu, and Xu Wei a） Department of Applied Mathematics, Northwestern Polytechnical University, Xi＇an 710072, China b） Department of Mathematics and Statistics, University of South Florida, Tampa FL 33620-5700, USA
Hirota bilinear form, Grammian and Pfaffian solutions, Wronski-type and Gramm-typePfaffian solutions
ISSN:1674-1056
2058-3834