Scipediacontent: Scipediacontent moved page Draft Content 391827554 to Hattam 2018a

2021-02-12T13:09:55Z

Scipediacontent moved page Draft Content 391827554 to Hattam 2018a

Scipediacontent: Created page with " == Abstract == A well-known optimal velocity (OV) model describes vehicle motion along a single lane road, which reduces to a perturbed modified Korteweg–de Vries (mKdV..."

2021-02-12T13:09:52Z

Created page with " == Abstract == A well-known optimal velocity (OV) model describes vehicle motion along a single lane road, which reduces to a perturbed modified Korteweg–de Vries (mKdV..."

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== Abstract ==

A well-known optimal velocity (OV) model describes vehicle motion along a single lane road, which reduces to a perturbed modified Korteweg–de Vries (mKdV) equation within the unstable regime. Steady travelling wave solutions to this equation are then derived with a multi-scale perturbation technique, where the travelling wave propagation coordinate depends upon slow and fast variables. The leading order solution in the hierarchy is then written in terms of these multi-scaled variables. At the following order, a system of differential equations is highlighted that govern the slowly evolving properties of the leading solution. Next, it is shown that the critical points of this system signify travelling waves without slow variation. As a result, a family of steady waves with constant amplitude and period are identified. When periodic boundary conditions are satisfied, these solutions’ parameters, including the wave speed, are associated with the driver’s sensitivity, a ˆ , which appears in the OV model. For some given a ˆ , solutions of both an upward and downward form exist, with the downward type corresponding to traffic congestion. Numerical simulations are used to validate the asymptotic analysis and also to examine the long-time behaviour of our solutions.

Document type: Article

== Full document ==
<pdf>Media:Draft_Content_391827554-beopen285-8605-document.pdf</pdf>

== Original document ==

The different versions of the original document can be found in:

* [http://arxiv.org/abs/1608.03488 http://arxiv.org/abs/1608.03488] under the license http://creativecommons.org/licenses/by-nc-nd/4.0

* [http://centaur.reading.ac.uk/75737/1/manuscript_hattam_reading.pdf http://centaur.reading.ac.uk/75737/1/manuscript_hattam_reading.pdf]

* [http://dx.doi.org/10.1016/j.wavemoti.2018.02.006 http://dx.doi.org/10.1016/j.wavemoti.2018.02.006] under the license http://creativecommons.org/licenses/by-nc-nd/4.0

* [https://api.elsevier.com/content/article/PII:S0165212518300611?httpAccept=text/xml https://api.elsevier.com/content/article/PII:S0165212518300611?httpAccept=text/xml],
: [https://api.elsevier.com/content/article/PII:S0165212518300611?httpAccept=text/plain https://api.elsevier.com/content/article/PII:S0165212518300611?httpAccept=text/plain],
: [http://dx.doi.org/10.1016/j.wavemoti.2018.02.006 http://dx.doi.org/10.1016/j.wavemoti.2018.02.006]

* [https://www.sciencedirect.com/science/article/pii/S0165212518300611 https://www.sciencedirect.com/science/article/pii/S0165212518300611],
: [http://ui.adsabs.harvard.edu/abs/2016arXiv160803488H/abstract http://ui.adsabs.harvard.edu/abs/2016arXiv160803488H/abstract],
: [http://centaur.reading.ac.uk/75737 http://centaur.reading.ac.uk/75737],
: [https://researchportal.bath.ac.uk/en/publications/travelling-wave-solutions-of-the-perturbed-mkdv-equation-that-rep https://researchportal.bath.ac.uk/en/publications/travelling-wave-solutions-of-the-perturbed-mkdv-equation-that-rep],
: [https://academic.microsoft.com/#/detail/2963391193 https://academic.microsoft.com/#/detail/2963391193] under the license https://www.elsevier.com/tdm/userlicense/1.0/

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Hattam 2018a - Revision history

Scipediacontent: Scipediacontent moved page Draft Content 391827554 to Hattam 2018a

Scipediacontent: Created page with " == Abstract == A well-known optimal velocity (OV) model describes vehicle motion along a single lane road, which reduces to a perturbed modified Korteweg–de Vries (mKdV..."