  Integration of nonlinear partial differential equations with the help of the
non-commutative integration over octonions is studied. An apparatus permitting
to take into account symmetry properties of PDOs is developed. For this purpose
formulas for calculations of commutators of integral and partial differential
operators are deduced. Transformations of partial differential operators and
solutions of partial differential equations are investigated. Theorems
providing solutions of nonlinear PDEs are proved. Examples are given.
Applications to PDEs of hydrodynamics and other types PDEs are described.
