  This paper develops a modification of the dressing method based on the
inhomogeneous linear integral equation with integral operator having nonempty
kernel. Method allows one to construct the systems of multidimensional Partial
Differential Equations (PDEs) having the differential polynomial forms in any
dimension n. Associated solution space is not full, although it is parametrized
by a certain number of arbitrary functions of (n-1)-variables. We consider
4-dimensional generalization of the classical (2+1)-dimensional S-integrable
N-wave equation as an example.
