Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems
patt-sol
2009-10-31 v1 Pattern Formation and Solitons
Abstract
In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham's solutions in the Newell's model. Our solutions can be used to describe temporal-spatial density patterns observed in the optimal velocity model for traffic flow.
Keywords
Cite
@article{arxiv.patt-sol/9810007,
title = {Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems},
author = {Yuji Igarashi and Katsumi Itoh and Ken Nakanishi},
journal= {arXiv preprint arXiv:patt-sol/9810007},
year = {2009}
}
Comments
Latex, 13 pages, 1 figure