Moving lattice kinks and pulses: an inverse method

Details Moving lattice kinks and pulses: an inverse method Moving lattice kinks and pulses: an inverse method

1998-12-08

arxiv.org/abs/patt-sol/9812004v2

Nonlinear Sciences

Pattern Formation and Solitons

15 pages, 5 figures

Scientific paper

10.1103/PhysRevE.59.6105

We develop a general mapping from given kink or pulse shaped travelling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping - by definition an inverse method - to acoustic solitons in chains with nonlinear intersite interactions, to nonlinear Klein-Gordon chains, to reaction-diffusion equations and to discrete nonlinear Schr\"odinger systems. Potential functions can be found in at least a unique way provided the pulse shape is reflection symmetric and pulse and kink shapes are at least $C^2$ functions. For kinks we discuss the relation of our results to the problem of a Peierls-Nabarro potential and continuous symmetries. We then generalize our method to higher dimensional lattices for reaction-diffusion systems. We find that increasing also the number of components easily allows for moving solutions.

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