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FIZIKA A 18 (2009) 4 , 153-164
 
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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