Exceptional discretisations of the sine-Gordon equation

I. V. Barashenkov; T. C. van Heerden

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arXiv · 0803.0603

Exceptional discretisations of the sine-Gordon equation

I. V. Barashenkov·T. C. van Heerden

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Abstract

Recently, the method of one-dimensional maps was introduced as a means of generating exceptional discretisations of the $ϕ^4$-theories, i.e., discrete $ϕ^4$-models which support kinks centred at a continuous range of positions relative to the lattice. In this paper, we employ this method to obtain exceptional discretisations of the sine-Gordon equation (i.e. exceptional Frenkel-Kontorova chains). We also use one-dimensional maps to construct a discrete sine-Gordon equation supporting kinks moving with arbitrary velocities without emitting radiation.

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I. V. Barashenkov, T. C. van Heerden. 2008-03-05. Exceptional discretisations of the sine-Gordon equation. https://arxiv.org/abs/0803.0603

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