KdV cnoidal waves in a traffic flow model with periodic boundaries

Hattam, L. L. (2017) KdV cnoidal waves in a traffic flow model with periodic boundaries. Physica D: Nonlinear Phenomena, 348. pp. 44-53. ISSN 0167-2789 doi: 10.1016/j.physd.2017.02.010

Abstract/Summary

An optimal-velocity (OV) model describes car motion on a single lane road. In particular, near to the boundary signifying the onset of traffic jams, this model reduces to a perturbed Korteweg-de Vries (KdV) equation using asymptotic analysis. Previously, the KdV soliton solution has then been found and compared to numerical results (see Muramatsu and Nagatani (1999)). Here, we instead apply modulation theory to this perturbed KdV equation to obtain at leading order, the modulated cnoidal wave solution. At the next order, the Whitham equations are derived, which have been modified due to the equation perturbation terms. Next, from this modulation system, a family of spatially periodic cnoidal waves are identified that characterise vehicle headway distance. Then, for this set of solutions, we establish the relationship between the wave speed, the modulation term and the driver sensitivity. This analysis is confirmed with comparisons to numerical solutions of the OV model. As well, the long-time behaviour of these solutions is investigated.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/69302
Identification Number/DOI	10.1016/j.physd.2017.02.010
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics > Centre for the Mathematics of Human Behaviour (CMOHB) Interdisciplinary centres and themes > Energy Research
Publisher	Elsevier
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