Discrete singular convolution for the sine-Gordon equation

This paper explores the utility of a discrete singular convolution (DSC) al gorithm 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 orb it. The present algorithm performs extremely well in terms of accuracy, eff iciency, simplicity, stability and reliability. (C) 2000 Elsevier Science B .V. All rights reserved.