Exact solutions to the nonlinear equation in traffic congestion

DOI10.1186/S13662-020-2538-XzbMath1482.76011OpenAlexW3029496221MaRDI QIDQ2057410

Qing Du, Damin Cao, Cheng Li

Publication date: 6 December 2021

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-020-2538-x

zbMATH Keywords

exact solutiontraveling wave solutionstraffic flowspace-time fractional equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Traveling wave solutions (35C07) Traffic and pedestrian flow models (76A30)

Cites Work

• Unnamed Item
• A transformed rational function method and exact solutions to the \(3+1\) dimensional Jimbo-Miwa equation
• Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations
• Empirical test of a microscopic three-phase traffic theory
• Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine-Cosine method
• Exact solutions for the generalized BBM equation with variable coefficients
• Solutions of the fractional combined KdV-mKdV equation with collocation method using radial basis function and their geometrical obstructions
• Nonlinear analysis of the optimal velocity difference model with reaction-time delay
• Optimal velocity difference model for a car-following theory
• Travelling wave solutions of the perturbed mKdV equation that represent traffic congestion
• A new definition of fractional derivative
• A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation
• Study on the effects of driver's lane-changing aggressiveness on traffic stability from an extended two-lane lattice model
• Interaction solutions to Hirota-Satsuma-Ito equation in (2 + 1)-dimensions
• Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation
• Classification of All Single Travelling Wave Solutions to Calogero–Degasperis–Focas Equation
• Traffic jams: dynamics and control
• Invariances and Conservation Laws of the Korteweg‐de Vries Equation
• Representations and Classification of Traveling Wave Solutions to sinh-Gördon Equation
• Solution of ODEu″ + p(u)(u′)²+q(u) = 0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations
• An Improved F-Expansion Method and Its Application to Coupled Drinfel'd–Sokolov–Wilson Equation
• Exact Solution of Space-Time Fractional Coupled EW and Coupled MEW Equations Using Modified Kudryashov Method
• A SEARCH FOR LUMP SOLUTIONS TO A COMBINED FOURTH-ORDER NONLINEAR PDE IN (2+1)-DIMENSIONS

This page was built for publication: Exact solutions to the nonlinear equation in traffic congestion