Group theoretic methods applied to Burgers' equation

摘要

In this study, the group-theoretic methods for calculating the solution of Burgers' equation with appropriate boundary- and initial-conditions is presented. The application of a one-parameter group reduces the number of independent variables by one, and consequently the governing partial differential equation with the boundary- and initial-conditions to an ordinary differential equation with the appropriate corresponding conditions. The obtained differential equation is solved analytically and the solution obtained in closed form, for a specific choice of boundary condition.