Hasebe, Katsuya; Nakayama, Akihiro; Sugiyama, Yūki Soliton solutions of exactly solvable dissipative systems. (English) Zbl 1011.34069 Comput. Phys. Commun. 142, No. 1-3, 259-262 (2001). 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. Reviewer: Jörg Härterich (Berlin) Cited in 1 Document 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) Keywords:traffic model; clustering; soliton PDF BibTeX XML Cite \textit{K. Hasebe} et al., Comput. Phys. Commun. 142, No. 1--3, 259--262 (2001; Zbl 1011.34069) Full Text: DOI OpenURL References: [1] () [2] Newell, G.F., Oper. res., 9, 2209, (1961) [3] Whitham, G.B., Proc. roy. soc. London A, 428, 49, (1990) · Zbl 0698.90030 [4] Y. Sugiyama, in [1] [5] Hasebe, K.; Nakayama, A.; Suigiyama, Y., Phys. lett. A, 259, 135, (1999) [6] Ablowitz, M.J.; Ladik, J.F., J. math. phys., 17, 1011, (1976) [7] Wadati, M., Prog. theor. phys. suppl., 59, 36, (1976) [8] Hirota, R.; Satsuma, J., Prog. theor. phys. suppl., 59, 64, (1976) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.