ON THE NUMERICAL-SOLUTION OF THE SINE-GORDON EQUATION .2. PERFORMANCEOF NUMERICAL SCHEMES

The phase space of sine-Gordon possesses tori and homoclinic structure s. It is important to determine how these structures are preserved by numerical schemes. In this, the second of two papers on the numerical solution of the sine-Gordon equation, we use the nonlinear spectrum as a basis for comparing the effectiveness of symplectic and nonsymplect ic integrators in capturing infinite dimensional phase space dynamics. In particular, we examine how the preservation of the nonlinear spect rum (i.e., the integrable structure) depends on the order of the accur acy and the symplectic property of the numerical scheme. (C) 1997 Acad emic Press.