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Soliton solutions of exactly solvable dissipative systems. (English) Zbl 1011.34069

Exact solutions to a car-following model are given under the assumption that the optimal velocity has a special explicit form. Numerical simulations indicate that these exact solutions in the form of Jacobi elliptic functions are stable.

MSC:

34K35 Control problems for functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
90B20 Traffic problems in operations research
34K13 Periodic solutions to functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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