On the numerical solution of the sine-Gordon equation

The phase space of sine-Gordon possesses tori and homoclinic structures. 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 nonsymplectic integrators in capturing infinite dimensional phase space dynamics. In particular, we examine how the preservation of the nonlinear spectrum (i.e., the integrable structure) depends on the order of the accuracy and the symplectic property of the numerical scheme. 19 refs., 20 figs., 1 tab