Some exact solutions to the Lighthill–Whitham–Richards–Payne traffic flow equations
Some exact solutions to the Lighthill–Whitham–Richards–Payne traffic flow equations
We find a class of exact solutions to the Lighthill–Whitham–Richards–Payne (LWRP) traffic flow equations. Using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either apply (again two) Lambert functions and obtain exact formulae for the dependence of the car density and velocity on …