Discrete singular convolution for the sine-Gordon equation

This paper explores the utility of a discrete singular convolution (DSC) algorithm for the integration of the sine-Gordon equation. The initial values are chosen close to a homoclinic manifold for which previous methods have encountered significant numerical difficulties such as numerically induced spatial and temporal chaos. A number of new initial values are considered, including a case where the initial value is “exactly” on the homoclinic orbit. The present algorithm performs extremely well in terms of accuracy, efficiency, simplicity, stability and reliability.