Abstract

Invariants for Generalised Burgers Equations

C.Sophocleous (Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus ); N.H.Ibragimov (Research Centre ALGA: Advances in Lie Group Analysis, Department of Health, Science and Mathematics, Blekinge Institute of Technology, Karlskrona, Sweden)

e-mail: christod@ucy.ac.cy

Recently, one of the authors (NHI) adopted the infinitesimal method for calculating invariants of families of differential equations using the equivalence groups. The method was employed first for understanding the group theoretic nature of the Laplace invariants for the linear hyperbolic partial differential equation and then to derive the Laplace type invariants for linear parabolic equations. The method was also applied to families of nonlinear equations. Here, we use the above method for calculating invariants of the family of generalised Burgers equations which has applications in acoustic phenomena and furthermore has been used to model turbulence and certain steady state viscous flows. The family of the equations in question involve one arbitrary function of time, and the equivalence group of the family is a certain representation of the projective group. We show that the invariant of this family of equations is a third-order differential invariant and is provided by the Schwarzian which has remarkable properties.

Section : 12