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Discrete singular convolution for the sine-Gordon equation. (English) Zbl 0944.35087

Summary: This paper explores the utility of a discrete singular convolution 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.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37L65 Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems
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