  In present paper we propose seemingly new method for finding solutions of
some types of nonlinear PDEs in closed form. The method is based on
decomposition of nonlinear operators on sequence of operators of lower orders.
It is shown that decomposition process can be done by iterative procedure(s),
each step of which is reduced to solution of some auxiliary PDEs system(s) for
one dependent variable. Moreover, we find on this way the explicit expression
of the first-order PDE(s) for first integral of decomposable initial PDE.
Remarkably that this first-order PDE is linear if initial PDE is linear in its
highest derivatives.
  The developed method is implemented in Maple procedure, which can really
solve many of different order PDEs with different number of independent
variables. Examples of PDEs with calculated their general solutions demonstrate
a potential of the method for automatic solving of nonlinear PDEs.
