1998/12/31 by S. Flach, Y. Zolotaryuk, K. Kladko · 1 citation
Physics and Astronomy · #patt-sol #nlin.PS
paper · pdf · doi:10.1103/physreve.59.6105
15 pages, 5 figures
arxiv created 1999/03/07 · arxiv updated 2009/11/30
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 Schrödinger 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 C2 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.