Non-local time evolution equation with singular integral and its application to traffic flow model

Fuente: arXiv

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Detalles Bibliográficos
Autor principal:	Higashi, Kohei
Formato:	Preprint
Publicado:	2024
Materias:	Exactly Solvable and Integrable Systems
Acceso en línea:	Acceder al recurso
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

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author	Higashi, Kohei
author_facet	Higashi, Kohei
contents	We consider an integro-differential equation model for traffic flow which is an extension of the Burgers equation model. To discuss the model, we first examine general settings for integrable integro-differential equations and find that they are obtained through a simple residue formula from integrable eqations in a complex domain. As demonstration of the efficiency of this approach, we list several integrable equations including a difference equation with double singular integral and an equation with elliptic singular integral. Then, we discuss the traffic model with singular integral and show that the model exhibits interaction between free flow region and congested region depending on the parameter of non-locality.
format	Preprint
id	arxiv_https___arxiv_org_abs_2402_13128
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Non-local time evolution equation with singular integral and its application to traffic flow model Higashi, Kohei Exactly Solvable and Integrable Systems We consider an integro-differential equation model for traffic flow which is an extension of the Burgers equation model. To discuss the model, we first examine general settings for integrable integro-differential equations and find that they are obtained through a simple residue formula from integrable eqations in a complex domain. As demonstration of the efficiency of this approach, we list several integrable equations including a difference equation with double singular integral and an equation with elliptic singular integral. Then, we discuss the traffic model with singular integral and show that the model exhibits interaction between free flow region and congested region depending on the parameter of non-locality.
title	Non-local time evolution equation with singular integral and its application to traffic flow model
topic	Exactly Solvable and Integrable Systems
url	https://arxiv.org/abs/2402.13128

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