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