Holonomic constraints and some exact solutions of the equations of steady one-dimensional gas flow

A first-order quasi-linear homogeneous system of equations with two depende nt and two independent variables is considered. Various one-dimensional ste ady gas flows can be modelled by systems of this type. The symmetries of th e system considered are used to construct holonomic constraints between the dependent (and independent) variables. The holonomic constraints between t he variables are used to reduce the dimension of the system and to construc t its exact solutions. (C) 2001 Elsevier Science Ltd. All rights reserved.