  We describe a variant of the dressing method giving alternative
representation of multidimensional nonlinear PDE as a system of
  Integro-Differential Equations (IDEs) for spectral and dressing functions. In
particular, it becomes single linear Partial Differential Equation (PDE) with
potentials expressed through the field of the nonlinear PDE. The absence of
linear overdetermined system associated with nonlinear PDE creates an obstacle
to obtain evolution of the spectral data (or dressing functions): evolution is
defined by nonlinear IDE (or PDE in particular case). As an example, we
consider generalization of the dressing method applicable to integrable
(2+1)-dimensional $N$-wave and Davey-Stewartson equations. Although represented
algorithm does not supply an analytic particular solutions, this approach may
have a perspective development.
