Painleve' analysis of a variable coefficient Sine-Gordon equation

In this paper we study a variable coefficient Sine-Gordon (vSG) equation given by theta(tt)-theta(xx)+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 well-defined 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)=F(1)(x+t)F(2)(x-t) where F(1)(x+t) and F(2)(x-t) are arbitrary functions. Using this last result we have obtained some particular solutions of the vSG equation. (c) 1995 American Institute of Physics.