New application to Riccati equation

doi:10.1088/1674-1056/19/8/080303

Abstract To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov–Kuznetsov equation, Karamoto–Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.

Keywords: Riccati equation formula of nonlinear superposition nonlinear evolution equation exact solution

Received: 19 September 2009
Revised: 14 December 2009
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	02.30.Hq	(Ordinary differential equations)
	02.30.Mv	(Approximations and expansions)
	02.30.Sa	(Functional analysis)
	02.70.Wz	(Symbolic computation (computer algebra))

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10461006), the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ07031), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 200408020103) and the Natural Science Research Program of Inner Mongolia Normal University, China (Grant No. QN005023).

Cite this article:

Taogetusang(套格图桑), Sirendaoerji(斯仁道尔吉), and Li Shu-Min(李姝敏) New application to Riccati equation 2010 Chin. Phys. B 19 080303

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