KdV cnoidal waves in a traffic flow model with periodic boundaries
| Autor: | Laura Hattam |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Modulation theory
Mathematical analysis FOS: Physical sciences Perturbation (astronomy) Cnoidal wave Statistical and Nonlinear Physics Dynamical Systems (math.DS) Pattern Formation and Solitons (nlin.PS) Condensed Matter Physics Traffic flow Nonlinear Sciences - Pattern Formation and Solitons 01 natural sciences 010305 fluids & plasmas Nonlinear Sciences::Exactly Solvable and Integrable Systems 0103 physical sciences Headway FOS: Mathematics Mathematics - Dynamical Systems Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons 010301 acoustics Mathematics |
| Zdroj: | Physica D: Nonlinear Phenomena. 348:44-53 |
| ISSN: | 0167-2789 |
| DOI: | 10.1016/j.physd.2017.02.010 |
| Popis: | 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 [1] ). 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. |
| Databáze: | OpenAIRE |
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