Convective Equations and a Generalized Cole-Hopf Transformation

TL;DR

This paper introduces a generalized Cole-Hopf transformation that links solutions of nonlinear convective differential equations, like Burger's equation, to linear equations, aiding in solving complex convection problems.

Contribution

It develops a generalized transformation method to connect nonlinear convective equations with linear ones, expanding analytical solution techniques.

Findings

Successfully relates generalized Burger's equations to linear equations

Provides a new approach for solving steady-state convection equations

Enhances analytical tools for nonlinear differential equations

Abstract

Differential equations with convective terms such as the Burger's equation appear in many applications and have been the subject of intense research. In this paper we use a generalized form of Cole-Hopf transformation to relate the solutions of some of these nonlinear equations to the solutions of linear equations. In particular we consider generalized forms of Burger's equation and second order nonlinear ordinary differential equations with convective terms which can represent steady state one-dimensional convection.