On the numerical solution of the sine-Gordon equation

Journal Article · Mon Jul 01 04:00:00 EDT 1996 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1996.0139· OSTI ID:447031

Ablowitz, M J; Schober, C ^[1]; Herbst, B M ^[2]

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1. Univ. of Colorado, Boulder, CO (United States)
2. Univ. of the Orange Free State, Bloemfontein (South Africa)

In this, the first of two papers on the numerical solution of the sine-Gordon equation, we investigate the numerical behavior of a double discrete, completely integrable discretization of the sine-Gordon equation. For certain initial values, in the vicinity of homoclinic manifolds, this discretization admits an instability in the form of grid scale oscillations. We clarify the nature of the instability through an analytical investigation supported by numerical experiments. In particular, a perturbation analysis of the associated linear spectral problem shows that the initial values used for the numerical experiments lie exponentially close to a homoclinic manifold. This paves the way for the second paper where we use the non-linear spectrum as a basis for comparing different numerical schemes. 21 refs., 11 figs.

• OSTI ID: 447031
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 126; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
NUMERICAL SOLUTION
SINE-GORDON EQUATION