中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70212-070212.doi: 10.1088/1674-1056/21/7/070212

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

唐亚宁a, 马文秀b, 徐伟a   

  1. 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
  • 收稿日期:2011-11-21 修回日期:2012-01-05 出版日期:2012-06-01 发布日期:2012-06-01
  • 基金资助:
    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.

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

Tang Ya-Ning(唐亚宁)a)†, Ma Wen-Xiu(马文秀) b), and Xu Wei(徐伟)a)   

  1. 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
  • Received:2011-11-21 Revised:2012-01-05 Online:2012-06-01 Published:2012-06-01
  • Contact: Tang Ya-Ning E-mail:tyaning@nwpu.edu.cn
  • Supported by:
    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.

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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.

关键词: Hirota bilinear form, Grammian and Pfaffian solutions, Wronski-type and Gramm-type Pfaffian solutions

Abstract: 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.

Key words: Hirota bilinear form, Grammian and Pfaffian solutions, Wronski-type and Gramm-type Pfaffian solutions

中图分类号:  (Other topics in mathematical methods in physics)

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