Group properties of a one-dimensional system of equations for wave propagation in various media (Q1116809)

The group properties and Lie algebra are derived for a one-dimensional system of equations modelling wave propagation in various media including viscoelastic and viscoplastic materials. The differential constitutive relation in this model contains an arbitrary function which affects the group structure. The restrictions of the group analysis imposed on the form of this constitutive law are described. Special attention is given to a quasi-linear differential form that models materials exhibiting a rate effect. In addition, the actions of specific one-parameter subgroups of the full Lie group on this system of equations are discussed.