Exceptional discretisations of the sine-Gordon equation

Details Exceptional discretisations of the sine-Gordon equation Exceptional discretisations of the sine-Gordon equation

2008-03-05

arxiv.org/abs/0803.0603v1

Nonlinear Sciences

Pattern Formation and Solitons

20 pages

Scientific paper

Recently, the method of one-dimensional maps was introduced as a means of generating exceptional discretisations of the $\phi^4$-theories, i.e., discrete $\phi^4$-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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