Di Garbo A., Fronzoni L. Painleve' analysis of a variable coefficient SineGordon equation. In: Chaos, vol. 5 (4) pp. 690  692. American Institute of Physics, 1995. 
Abstract (English) 
In this paper we study a variable coefficient SineGordon (vSG) equation given by thetatt−thetaxx+F(x,t)sin theta=0 where F(x,t) is a real function. To establish if it may be integrable we have performed the standard test of Weiss, Tabor, and Carnevale (WTC). We have got that the (vSG) equation has the Painleve' property (Pp) if the function F(x,t) satisfies a welldefined nonlinear partial differential equation. We have found the general solution of this last equation and, consequently, the functions F(x,t) such that the (vSG) equation possesses the (Pp), are given by F(x,t)=F1(x+t)F2(x−t) where F1(x+t) and F2(x−t) are arbitrary functions. Using this last result we have obtained some particular solutions of the 

DOI:  10.1063/1.166144  
Subject  Painleve' analysis SineGordon equation 
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