Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems
- 15 March 1999
- journal article
- Published by Physical Society of Japan in Journal of the Physics Society Japan
- Vol. 68 (3) , 791-796
- https://doi.org/10.1143/jpsj.68.791
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.Comment: Latex, 13 pages, 1 figurKeywords
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