Symmetry in the problem of wave modes of thin viscous liquid layer flow

The equations in conservative form for modelling nonlinear waves on a liquid film flowing down a vertical plane have been investigated. It has been found out that the equations with boundary conditions are invariant under parity transformation in the extended computational domain. The steady-state travelling solutions are numerically shown to have the detected symmetry for moderate Reynolds numbers. The use of this symmetry for the numerical solution of the problem by Galerkin methods significantly increases the efficiency of calculations.