Application Of The Jacobi Elliptic Function Expansion Method To The Full Velocity Difference Model And Its Time Delay Model

As people’s living standards improve,the demand of whole society to traffic transportation is increasing more and more.However,the traffic demand increases faster than construction for road infrastructure.This constitutes a very prominent contradictions and results in traffic congestion which becomes an urgent problem to be solved.In order to control the traffic flow effectively,many scholars try to solve traffic flow models with a variety of methods.In this dissertation,we apply a discrete form of the Jacobi elliptic function expansion method to solve the full velocity difference model and its delayed model for the first time.We obtain the following main results:Firstly,by introducing three kinds of Jacobi elliptic function solutions to the full velocity difference model,we get a group of over-determined equations.After solving the derived over-determined equations with aid of the Maple software programming.we obtain five new group of solitary wave solutions of the full velocity difference model.Secondly,we solve the full velocity difference model with time delay by using the Jacobi elliptic function expansion method.After solving several particular solutions of the derived over-determined equations which are derived from solving the nonlinear equations,we obtain many new group of solitary wave solutions of the full velocity difference model with time delay and that the solutions are lesser under than the model without time delay.For this,we make a constant assumption so as to obtain more solutions.