Lie symmetries of generalized Burgers equations: application to boundary-value problems

摘要

There exist several approaches exploiting Lie symmetries in the reduction of boundary-value problems for partial differential equations modelling real-world phenomena to those problems for ordinary differential equations. Using an example of generalized Burgers equations appearing in non-linear acoustics we show that the direct procedure of solving boundary-value problems using Lie symmetries first described by Bluman is more general and straightforward than the method suggested by Moran and Gaggioli [J Eng Math 3:151-162, 1969]. After performing group classification of a class of generalized Burgers equations with time-dependent viscosity we solve an associated boundary-value problem using the symmetries obtained.