Exceptional discretisations of the sine-Gordon equation
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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.
20 pages
20 pages