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A novel lattice traffic flow model and its solitary density waves. (English) Zbl 1263.82014
Summary: A novel lattice traffic flow model with a slope effect is proposed. Neutral stability condition is obtained by the use of the linear stability theory. The standard KdV equation is derived in the meta-stable region and soliton solution is obtained near the neutral stability line. The solitary waves are reproduced through the numerical simulations. Results show that the solitary density wave appears in upward form when the average density is less than critical density, otherwise it exhibits downward form.
MSC:
82B20Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
90B20Traffic problems
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations