Reduction of nonhomoheneous quasilinear 2x2 systems to homogeneous and autonomous form

By using the invariance with respect to suitable Lie groups of point transformations, necessary and sufficient conditions are determined allowing one to map through an invertible point transformation nonhomogeneous and nonautonomous quasilinear 22 systems to homogeneous and autonomous form. The procedure is constructive and the new independent and dependent variables are obtained by determining the canonical variables associated with the Lie groups of point symmetries admitted by the source system. Various examples of physical interest arising from different contexts are considered.