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

doi:10.1088/1674-1056/20/9/090203

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.

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

Received: 18 March 2011
Revised: 19 April 2011
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	47.10.-g	(General theory in fluid dynamics)
	02.20.Hj	(Classical groups)
	02.30.Mv	(Approximations and expansions)

Cite this article:

Liu Ping(刘萍) and Fu Pei-Kai(付培凯) Modified (2+1)-dimensional displacement shallow water wave system and its approximate similarity solutions 2011 Chin. Phys. B 20 090203

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

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