Travelling wave solutions of a one-dimensional viscoelasticity model

In this paper a one-dimensional viscoelasticity model describing the behaviour of a one-dimensional viscoelastic medium is studied through Lie symmetry approach. The infinitesimals of the group of transformations leaving the equation invariant are determined. The optimal systems of one-dimensional subalgebras of the Lie symmetry algebras are calculated. Afterwards, using the Lie symmetry approach, we transformed the nonlinear partial differential equation into a nonlinear ordinary differential equation. Furthermore, we applied the -expansion method to find explicitly new travelling wave solutions. Moreover, some conservation laws are constructed by applying the multiplier method.