On the Solution of Burgers’ Equation with Forcing Terms

Abstract

In this article, we solve exactly the Burgers equation with non-homogeneous terms using the Cole–Hopf type transformation. The Cole–Hopf transformation changes the classical Burgers equation to a linear equation. We modify the Cole–Hopf transformation, introducing a time dependent function to linearise the non-homogeneous Burgers equations. We consider a group of non-homogeneous terms based on the function introduced in the modified Cole–Hopf transformation. We present a list of twenty five exact solutions for non-homogeneous Burgers equations. Our study reveals that the use of the Cole–Hopf type transformation combined with the exact solutions of the heat equation can provide the exact solutions for non-homogeneous Burgers equations. This indicates the potential of the Cole–Hopf type transformation in solving nonlinear partial differential equations.

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