Lie Group Analysis of the Time-delayed Inviscid Burgers' Equation

Abstract

In this paper, we discuss group analysis of first-order delay partial differential equations and use it to obtain symmetries of the inviscid Burgers' equation with delay, its kernel and extensions of the kernel. We obtain a Lie type invariance condition for first-order delay partial differential equations by using Taylor's theorem for a function of several variables. We obtain the symmetries admitted by this delay partial differential equation. Further, we obtain representations of analytic solutions and the reduced equations from the symmetries