Exceptional discretizations of the sine-Gordon equation.
The method of one-dimensional maps was recently introduced as a means of generating exceptional discretizations of the phi(4) theory, i.e., discrete phi(4) models which support kinks centered at a continuous range of positions relative to the lattice. In this paper, we employ this method to obtain exceptional discretizations 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 which move with arbitrary velocities without emitting radiation.
Department of Mathematics, University of Cape Town, Rondebosch, South Africa. igor.barashenkov@uct.ac.za
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van Heerden