THE (2-DIMENSIONAL SINE-GORDON EQUATION - INTEGRABILITY AND LOCALIZEDSOLUTIONS(1))

In this paper, the (2 + 1)-dimensional sine-Gordon equation (2DSG) int roduced by Konopelchenko and Rogers is investigated and is shown to sa tisfy the Painleve property. A variable coefficient Hirota bilinear fo rm is constructed by judiciously using the Painleve analysis with a no n-conventional choice of the vacuum solutions. First the line kinks ar e constructed. Then, exact localized coherent structures in the 2DSGI equation are generated by the collision of two non-parallel ghost soli tons, which drive the two non-trivial boundaries present in the system . Also the reason for the difficulty in identifying localized solution s in the 2DSGII equation is indicated. We also highlight the significa nce of the asymptotic values of the boundaries of the system.