FIZIKA A 18 (2009) 4 , 153-164

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SOME NOTES ON PROJECTIVE RICCATI EQUATION METHOD

XINGHUA DU
Department of Mathematics, Daqing Petroleum Institute, Daqing 163318, China
E-mail address: xinghuadu@126.com

 Received 15 December 2008;    Revised manuscript received 13 November 2009
Accepted 18 November 2009    Online 7 December 2009

In this paper, several aspects of projective Riccati equation method are discussed. Firstly, according to the scheme of routine projective Riccati equation method, a united scheme of projective Riccati equation method is proposed, and its mathematical foundation is studied. Secondly, some no-go theorems and positive results are obtained. The limitations of projective Riccati equation method are found. In particular, in the end, we point out that some solutions obtained by the projective Riccati equation method to some equations in a reference are not solutions at all.

PACS numbers: 05.45.Yv, 03.65.Ge, 02.30.Jr
UDC 531.553, 531.26

Keywords: projective Riccati equation method, elementary integral method, nonlinear differential equation, traveling wave solution

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