Conservation laws of one-dimensional strain-limiting viscoelasticity model

For a model describing the behaviour of one-dimensional viscoelastic medium, all conservation laws are constructed. From a nonlinear partial differential equation, which describes the model, the conservation laws are derived by using the multipliers method. Furthermore, the Lie point symmetries of the equation and the Lie point symmetries associated with the conserved vectors are determined. Then, the classical symmetries are obtained by the Lie classical method. Finally, in order to find potential symmetries, the associated auxiliary system is obtained. However, applying the classical method to the associated auxiliary system yields to the classical symmetries too.