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

作　　者：唐亚宁 马文秀 徐伟 

机构地区：[1]Department of Applied Mathematics,Northwestern Polytechnical University [2]Department of Mathematics and Statistics,University of South Florida

出　　处：《Chinese Physics B》2012年第7期85-91,共7页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant Nos. 10932009 and 11172233);the Northwestern Polytechnical University Foundation for Fundamental Research, China (Grant No. GBKY1034);the State Administration of Foreign Experts Affairs of China, and the Chunhui Plan of the Ministry of Education of China

摘　　要：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.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.

关 键 词：Hirota bilinear form Grammian and Pfaffian solutions Wronski-type and Gramm-typePfaffian solutions 

分 类 号：O411.1[理学—理论物理] TV139.231[理学—物理]