中国物理B ›› 2011, Vol. 20 ›› Issue (9): 90203-090203.doi: 10.1088/1674-1056/20/9/090203

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Modified (2+1)-dimensional displacement shallow water wave system and its approximate similarity solutions

付培凯1, 刘萍2   

  1. (1)Academic Affairs Division, Zhongshan Polytechnic, Zhongshan 528404, China; (2)Department of Electronic Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, China
  • 收稿日期:2011-03-18 修回日期:2011-04-19 出版日期:2011-09-15 发布日期:2011-09-15

Modified (2+1)-dimensional displacement shallow water wave system and its approximate similarity solutions

Liu Ping(刘萍)a)† and Fu Pei-Kai(付培凯)b)   

  1. a Department of Electronic Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, China; b Academic Affairs Division, Zhongshan Polytechnic, Zhongshan 528404, China
  • Received:2011-03-18 Revised:2011-04-19 Online:2011-09-15 Published:2011-09-15

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摘要： Recently, a new (2+1)-dimensional shallow water wave system, the (2+1)-dimensional displacement shallow water wave system (2DDSWWS), was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev—Petviashvili equation and Korteweg—de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS (M2DDSWWS) is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.

关键词: modified (2+1)-dimensional displacement shallow water wave system, viscidity, approximate similarity solutions, Kadomtsev—Petviashvili equation

Abstract: Recently, a new (2+1)-dimensional shallow water wave system, the (2+1)-dimensional displacement shallow water wave system (2DDSWWS), was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev—Petviashvili equation and Korteweg—de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS (M2DDSWWS) is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.

Key words: modified (2+1)-dimensional displacement shallow water wave system, viscidity, approximate similarity solutions, Kadomtsev—Petviashvili equation

中图分类号:  (Partial differential equations)

  • 02.30.Jr
47.10.-g (General theory in fluid dynamics) 02.20.Hj (Classical groups) 02.30.Mv (Approximations and expansions)