Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN(2013)
摘要
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.
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关键词
toda lattice solutions,differential-difference equations,optimal velocity model,temporal-spatial density patterns
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